Electrophoretic separation control method based on ET zone diffusion model

Abstract

The invention discloses an electrophoretic separation control method based on an ET zone diffusion model. The electrophoretic separation control method comprises the following steps: establishing the ET zone diffusion model; substituting the operation time t and the electric field intensity E by using an ET zone diffusion model to calculate a gap G between the two zones; and judging whether GE separation is successful or not according to the size of the gap G. According to the electrophoretic separation control method, separation gaps are accurately controlled by selecting proper electric field intensity (E) and electrophoresis time (t), preoperative planning of GE separation is achieved, the separation effect under different conditions can be rapidly predicted, the method has the advantages of being high in resolution ratio, high in separation efficiency, high in speed and the like, theoretical guidance is provided for accurate control over GE separation, and the method is suitable for large-scale popularization and application. The method has important application value in the technical field of biomedical separation and analysis.

Description

Technical Field

[0001] The invention belongs to the technical field of biomedical separation and analysis, and in particular to an electrophoresis separation control method based on an ET zone diffusion model. Background Art

[0002] As the most commonly used electrophoretic separation model, zone electrophoresis has been widely used in the separation and analysis of ions, compounds, proteins, nucleic acids, viruses, nanoparticles, and cells. There are many different types of zone electrophoresis separation media. Depending on the separation medium or carrier, it is divided into agarose gel zone electrophoresis, polyacrylamide gel zone electrophoresis, capillary zone electrophoresis, and chip zone electrophoresis. Regardless of the separation mode, the basic separation principle of zone electrophoresis is:

[0003] x(t)=μEt

[0004] In the above formula, x(t) represents the peak position of the migration band at time point t, while μ and E represent the electrophoretic mobility and electric field strength of the solution, respectively.

[0005] At present, many scholars have conducted research on improving the efficiency of zone electrophoresis. For example, capillary electrophoresis is used to improve the separation efficiency of traditional gel electrophoresis, and physical cooling devices such as fluorocarbon liquid cooling systems, thermoelectric cooling systems, and metal heat dissipation modules are designed to improve the separation efficiency of zone electrophoresis. These methods have accelerated the separation of zone electrophoresis. In addition, in order to further explore the mechanism of zone diffusion, especially the relationship between operation time, temperature and diffusion bandwidth in GE systems, relevant prior art has shown that zone diffusion can be controlled by two factors: operation time and temperature, revealing that lower temperature and faster operation time can lead to steeper bandwidth. The analysis of the zone diffusion mechanism proposed in the prior art provides valuable theoretical support for solving the challenges associated with low resolution in GE. However, it is important to note that neither temperature nor Joule heating are directly controllable variables in GE systems. This prompted the inventors of the present application to consider whether common control parameters (such as electric field strength and operation time) can be used to develop a temperature-independent model to clarify the mechanism behind the changes in zone position and bandwidth, thereby achieving precise control of GE separation of substances. Summary of the Invention

[0006] The purpose of the invention is to provide an electrophoresis separation control method based on the ET zone diffusion model, which can accurately control the separation gap by selecting appropriate electric field strength and running time, thereby achieving precise control of GE separation of substances.

[0007] Technical solution: The electrophoretic separation control method based on the ET zone diffusion model of the present invention comprises the following steps:

[0008] Step 1, establish the ET zone diffusion model;

[0009] Step 2: Set the running time t and the electric field strength E, and then use the ET zone diffusion model to calculate the gap G between the two zones by inputting the running time t and the electric field strength E;

[0010] Step 3: Determine whether the GE separation is successful based on the size of the gap G. If G is less than zero, it means that the zones overlap and the separation is unsuccessful. If G is greater than zero, it means that the zones are successfully separated.

[0011] Furthermore, in step 1, the established ET zone diffusion model includes a zone migration position model and a bandwidth calculation model; wherein the migration position model is:

[0012]

[0013] Where μ and E represent the electrophoretic mobility and electric field strength of the solution, respectively. represents the peak position of band migration at time point t;

[0014] The bandwidth calculation model is:

[0015]

[0016] Where a, b, and c i (i=0,1,…,n) are all constant coefficients of the model.

[0017] Furthermore, when calculating the three constant coefficients, the calculation formula of the constant coefficient a is:

[0018]

[0019] Where, σ0 is the initial zone variance;

[0020] The calculation formula of the constant coefficient b is:

[0021]

[0022] Where z and e are the ion valence and electron charge, respectively, k represents the Boltzmann constant, and T0 is the ambient temperature;

[0023] Constant coefficient c i The calculation formula is:

[0024]

[0025] Where R is the equivalent resistance of the gel, d is the distance between the positive and negative electrodes, and x i is a constant coefficient.

[0026] Furthermore, in step 2, the formula for calculating the gap G between two zones is:

[0027]

[0028] Where, and are the migration positions of the central peaks of the two zones (calculated by the migration position model), and are the bandwidths of the central peaks of the two zones (calculated by the bandwidth calculation model).

[0029] Furthermore, in step 2, the bandwidth calculation model is optimized according to the zone width approximation effect of the bandwidth calculation model, and the optimized bandwidth calculation model is obtained as follows:

[0030]

[0031] Where, x0, x0 is a constant coefficient, and the optimized bandwidth calculation model is used as the final bandwidth calculation model.

[0032] Compared with the prior art, the present invention has the following beneficial effects: the electrophoresis separation control method proposed in the present invention allows for precise control of the separation gap by selecting appropriate electric field strength (E) and electrophoresis time (t). Since electric field strength (E) and electrophoresis time (t) are simple control parameters in gel electrophoresis (GE), the position and width of the zone can be predicted, thereby enabling preoperative planning of GE separation. The ET zone diffusion model obtained by the method of the present invention can quickly predict the separation effect under different conditions, provides theoretical guidance for precise control of GE separation, and has important application value in the field of biomedical separation and analysis technology. Compared with existing zone electrophoresis, the proposed method allows for precise control of the separation gap by selecting appropriate electric field strength (E) and electrophoresis time (t), and has the advantages of high resolution, high separation efficiency and high speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a flow chart of the method of the present invention;

[0034] Figure 2 This is a schematic diagram of GE material separation according to the present invention;

[0035] Figure 3 The relationship between the gap G, the running time t and the electric field strength E of the invention;

[0036] Figure 4 This is a diagram showing the band position and bandwidth fitting results of the ET zone diffusion model of the rice receptor protein kinase gene of the present invention;

[0037] Figure 5Graph showing the results of separating nucleic acid samples (CERK1 and CEBiP) using a flat-plate GE system under different electric fields and operating times according to the present invention;

[0038] Figure 6 Four ET zone diffusion models (A) and a temperature-dependent model (B) were compared for the bandwidth fitting results of the present invention. DETAILED DESCRIPTION

[0039] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0040] like Figure 1 As shown, the electrophoresis separation control method based on the ET zone diffusion model disclosed in the present invention includes the following steps:

[0041] Step 1, establish the ET zone diffusion model;

[0042] Step 2: Set the running time t and the electric field strength E, and then use the ET zone diffusion model to calculate the gap G between the two zones by inputting the running time t and the electric field strength E;

[0043] Step 3: Determine whether the GE separation is successful based on the size of the gap G. If G is less than zero, it means that the zones overlap and the separation is unsuccessful. If G is greater than zero, it means that the zones are successfully separated.

[0044] Furthermore, in step 1, the established ET zone diffusion model includes a zone migration position model and a bandwidth calculation model; wherein the migration position model is:

[0045]

[0046] Where μ and E represent the electrophoretic mobility and electric field strength of the solution, respectively. represents the peak position of band migration at time point t;

[0047] The bandwidth calculation model is:

[0048]

[0049] Where a, b, and c i (i=0,1,…,n) are all constant coefficients of the model.

[0050] Furthermore, when calculating the three constant coefficients, the calculation formula of the constant coefficient a is:

[0051]

[0052] Where, σ0 is the initial zone variance;

[0053] The calculation formula of the constant coefficient b is:

[0054]

[0055] Where z and e are the ion valence and electron charge, respectively, k represents the Boltzmann constant, and T0 is the ambient temperature;

[0056] Constant coefficient c i The calculation formula is:

[0057]

[0058] Where R is the equivalent resistance of the gel, d is the distance between the positive and negative electrodes, and x i is a constant coefficient.

[0059] Furthermore, in step 2, the formula for calculating the gap G between two zones is:

[0060]

[0061] Where, and are the migration positions of the central peaks of the two zones (calculated by the migration position model), and are the bandwidths of the central peaks of the two zones (calculated by the bandwidth calculation model).

[0062] Furthermore, in step 2, the bandwidth calculation model is optimized according to the zone width approximation effect of the bandwidth calculation model, and the optimized bandwidth calculation model is obtained as follows:

[0063]

[0064] Where, x0, x0 is a constant coefficient, and the optimized bandwidth calculation model is used as the final bandwidth calculation model.

[0065] The specific derivation process of the bandwidth calculation model of the present invention is as follows:

[0066] First, the basic separation principle of zone electrophoresis is:

[0067] x(t)=μEt (1)

[0068] In formula (1), x(t) represents the peak position of the migration band at time point t, while μ and E represent the electrophoretic mobility and electric field strength of the solution, respectively.

[0069] In GE operation, the position and width of the zone migration are defined as:

[0070] x(t)=μEt (2)

[0071]

[0072] In equation (2), x(t) represents the peak position of the band migration at time point t, while μ and E represent the electrophoretic mobility and electric field strength of the solution, respectively. In equation (3), σ0 refers to the initial band variance, k represents the Boltzmann constant, T represents the absolute temperature, z and e represent the ion valence and electron charge, respectively, and μ has the same meaning as in equation (1). σ0, k, μ, z, and e are constants or approximate constants.

[0073] From equations (1) and (2), we can see that the position and bandwidth depend on temperature and run time. However, the temperature in a gel electrophoresis (GE) system is affected by various factors, making it difficult to control and maintain the stability of the instrument.

[0074] According to the principle of conservation of heat exchange, the dynamic heat transfer in the gel during GE operation can be expressed as follows:

[0075] Q cp =Q Joule -Q diss (4)

[0076] where Q cp , Q Joule and Q diss are heat accumulation, Joule heat, and dissipated heat in the gel and buffer, respectively. Heat accumulation is expressed as follows:

[0077] Q cp =c p m(T′-T0′) (5)

[0078] Among them, c p is the specific heat capacity at constant pressure, m is the mass of the substance, T′ is the temperature of the gel and buffer, T0′ is their initial temperature, and Joule heat is expressed as follows:

[0079] Q Joule =I 2 Rt(6)

[0080] I is the current, R is the resistance, and t is the time. Heat dissipation occurs primarily through conduction, convection, and radiation. It is worth noting that radiation generally plays a minor role in heat dissipation at lower temperatures, such as those encountered during electrophoresis. Therefore, the following equation (7) can be used to simulate heat dissipation under electrophoresis conditions:

[0081] Q diss =Q cond +Q conv (7)

[0082] Among them, Q cond and Q conv represent heat dissipation by conduction and convection respectively.

[0083] According to Fourier's law of heat conduction, the change of heat conductivity in the gel with time t can be expressed as follows:

[0084]

[0085] Among them, k cond is the thermal conductivity of the gel, A cond is the gel area, T is the gel temperature, T RT is the ambient temperature, and d is the thickness of the gel.

[0086] Newton's law of cooling states that the heat dissipated by convection is expressed as:

[0087] Q conv =hA conv (TT RT )t(9)

[0088] Where h is the convective heat transfer coefficient, A conv is the heat dissipation surface area, T and T RT The meaning of is the same as in formula (8).

[0089] Assuming that the gel and buffer are placed in the experimental environment for sufficient heat exchange to reach equilibrium, T0 is equal to T RT Substituting into equations (5) to (9), we get T RT =T0 is substituted into formula (4), then:

[0090]

[0091] Equation (10) can be further expressed as a function of temperature T:

[0092]

[0093] Assuming that t1 is the observation timestamp during GE operation, the Taylor series expansion of Equation (11) at t = t1 is:

[0094]

[0095]

[0096] In formula (12), except I 2 Except for R and t, all elements are constants or can be considered as constants, then Equation (12) can be simply rewritten as a polynomial sum:

[0097] T≈T0+x0I 2 R+x1I 2 Rt+x2I 2 Rt 2 +…+x nI 2 Rt n (13)

[0098] Where x0~x n is a constant coefficient. Substituting equation (13) into equation (3), we get the bandwidth spread estimate:

[0099]

[0100] According to Ohm's law, V = IR, where V is the voltage. When the GE operates under a uniform electric field, V = Ed, where E and d are the electric field strength and the distance between the positive and negative electrodes, respectively. R is the equivalent resistance of the gel and can be considered a constant during GE operation. Equation (14) can then be further written as:

[0101]

[0102] There is a constant a:

[0103]

[0104] And for a given buffer with a certain pH value, the mobility μ and the ion valence z are constants, resulting in constants b and c i for:

[0105]

[0106]

[0107] Therefore, by substituting equations (16) to (18) into equation (14), the bandwidth of the zonal diffusion model in equation (19) is estimated as:

[0108]

[0109] Equation (19) reveals the complex relationship between the bandwidth w, the electric field strength E, and the electrophoresis time t, and enables the estimation of the zone width w. In addition, the migration position of the zone can be estimated using Equation (20):

[0110]

[0111] During GE operation, the electric field is uniform and the gel remains unchanged. Equations (19) and (20) represent the electric field and time-driven (ET) zone diffusion models, respectively. It is worth noting that experimental results confirm that the first three terms of Equation (19) can well approximate the zone width w. Therefore, Equation (21) is applied to actual GE operation:

[0112]

[0113] The ET zone diffusion model proposed in this invention can accurately determine the separation boundary between two substances. Given the running time t and the electric field strength E, the gap G can be accurately calculated. Figure 3 The relationship between G, t, and E is shown. The red separation boundary divides the ET zone diffusion model into two parts: the upper separable part, where each point corresponds to a G greater than zero, indicating that the zones are successfully separated with a gap of G under the electric field strength E at time t; and the lower non-separable part, where G is less than zero, indicating that the zones overlap and separation is unsuccessful.

[0114] like Figure 4 As shown, the electrophoretic behavior of two nucleic acid samples (i.e., rice receptor protein kinase genes CERK1 and CEBiP) was analyzed using the ET zone diffusion model proposed in this paper. The experimental setup involved running the treated samples through GE on our system for 12 minutes at electric field strengths ranging from 5 V / cm to 17.5 V / cm. Figure 4 (A) is the actual band position, bandwidth and fitting model of CERK1 (sample 1), Figure 4 (B) The actual band position, bandwidth and fitting model of CEBiP (sample 2).

[0115] Figure 4 (A) Shows the actual CERK1 band position and bandwidth measured during the GE run, along with the corresponding fitted surface obtained using the proposed ET zone diffusion model. The left subfigure shows the experimental results of the sample migration distance (x(t)) during gel electrophoresis as a function of electric field strength (E) and run time (t). This surface is a model fit based on the migration position model for the actual data. -4 Band location modeling showed a high correlation between the observed data and the model predictions, with an Adjusted R² value of 0.998. The model fit exhibited a low RMSE of 0.036, indicating minimal deviation from the observed data. Furthermore, the AIC value of -170.0 further confirmed the model's suitability, indicating a good balance between model complexity and fit quality. The right subplot shows the squared bandwidth (w 2 ) and the experimental results of the relationship between E and t. Fitting model based on bandwidth calculation model Expressed as The model shows a quadratic relationship with the electric field intensity and a linear relationship with the running time. The adjusted R2 of the model is 0.973, indicating that there is a high correlation between the modeled value and the observed data, which explains the changes in the electric field intensity and running time. The RMSE of the model is 1.201×10 -7, indicating that the fit is very accurate and the model predictions match the empirical data points very well. The AIC value of -2480.9 strongly supports the validity of the model. Figure 4 (B) shows the fitting results of CEBiP under the same experimental conditions as CERK1. The model predictions are highly consistent with the experimental observations. The adjusted R2 for the band position and bandwidth are 0.988 and 0.975, respectively. The RMSE is very low, 0.006 and 1.045×10 -7 The AIC values ​​are negative and large, at -446.5 and -2502.6, respectively.

[0116] All data further confirm the statistical robustness of the proposed ET zone diffusion model and its applicability to elucidating the electrophoretic behavior of nucleic acids in gel electrophoresis, particularly for describing band positions and widths. The proposed new model provides a reliable quantitative tool for analyzing the diffusion properties of GE run bands under different electrophoretic conditions.

[0117] To verify the effectiveness of the gap model in predicting the separation of two nucleic acids, CERK1 and CEBiP, we performed separation experiments using the same samples as in previous experiments. The position and bandwidth parameters required for the gap G prediction were derived from the ET zone diffusion model previously fitted to these substances. Experiments were designed to test conditions of no separation, complete separation, and near the separation boundary. The results of these experiments are shown in Figure 2. Figure 5 shown.

[0118] Figure 5 Figures AF show the electrophoretic band patterns of samples under specific conditions: (A) E = 7.5 V / cm (U = 60 V), t = 1200 s, (B) E = 10 V / cm (U = 80 V), t = 1200 s, (C) E = 12.5 V / cm (U = 100 V), t = 840 s, (D) E = 15 V / cm (U = 120 V), t = 660 s, (E) E = 17.5 V / cm (U = 140 V), t = 480 s, and (F) E = 15 V / cm (U = 120 V), t = 1000 s. (G) The relationship between the measured band gap and the model of Eq. The red circles indicate the model predictions, and the green inverted triangles indicate the experimentally measured gaps. The AE indices indicate the data points corresponding to the gap intervals in panels A and B, respectively.

[0119] Electrophoretic separation of nucleic acid samples CERK1 and CEBiP using a flatbed GE system at different electric fields and run times. Panels A to F show the banding patterns obtained from the electrophoresis, and fluorescence images were analyzed using ImageJ software. Figure 5 A failed to achieve separation of the two substances under the conditions of E=7.5V / cm (U=60V) and t=1200s. Figure 5F shows that the sample is completely separated at E = 15 V / cm (U = 120 V) and t = 1000 s. Figure 5 BE represents the conditions that precisely achieve a sharp separation. These conditions were optimized using either higher electric field strengths and shorter run times or lower electric fields and longer run times. The specific settings for these experiments were calculated based on the formula for the gap G to locate them near the separation boundary. Figure 5 G shows the superposition of the actual measured band gap and the theoretical prediction of the gap model. The red circle marks indicate the model prediction, while the green inverted triangle marks indicate the experimentally measured band gap. The labels AE correspond to Figure 5 Experimental setup in AE. Under BF conditions, the average error and standard deviation of the model predictions were 0.019 mm ± 0.012 mm, demonstrating remarkable agreement between the experimental data and the model predictions. This consistency highlights the model's ability to effectively predict separation behavior under a variety of experimental configurations. Together, these results not only validate the reliability of the gap model but also highlight its utility as a quantitative tool for optimizing electric field strength and run time parameters to achieve targeted separation outcomes.

[0120] Based on the assumption of electric field uniformity and the stability of substances during electrophoresis, a new ET zone diffusion model was developed. Through thermodynamic analysis and theoretical derivation, the band position and bandwidth are uniformly expressed in terms of electric field intensity and time, facilitating the optimization of ET parameters. This allows for flexible control of electrophoresis by using the t in actual systems. Figure 6 and Table 1 shows the comparison of these three models.

[0121] analyze Figure 4 、 Figure 6 As shown in Table 1, the three- and four-term ET zonal diffusion models exhibit higher Adjusted R² values ​​and lower RMSE (Residual Value Error) compared to the temperature-dependent model, where E is a stable, noise-free control variable. Although the four-term ET zonal diffusion model has a slightly lower RMSE, it is more complex due to the inclusion of the E²t term. The coefficient of this term is very small and may not significantly affect model performance.

[0122] Furthermore, the three-term ET zonal diffusion model achieved the lowest AIC value, indicating a better balance between simplicity and accuracy. It achieved a high Adjusted R² and a relatively low RMSE, making it a better choice for avoiding overfitting. As shown in Table 1, the three-term model achieved good AIC values ​​of -2480.9 (SP1) and -2502.6 (SP2), while maintaining high Adjusted R² values ​​of 0.973 (SP1) and 0.975 (SP2). Therefore, in practical engineering applications, we recommend the simpler three-term ET zonal diffusion model, as it provides accurate results with fewer parameters, thereby minimizing the risk of overfitting.

[0123] Table 1. Comparison of detailed indicators of the zonal diffusion model (data and Figure 4 and Figure 6 SP1 and SP2 represent sample 1 and sample 2 respectively)

[0124]

[0125] The new ET zone diffusion model was further validated using a newly designed flat-panel GE system. By measuring the real-time fluorescence band position and bandwidth and determining model parameters related to material properties, the ET zone diffusion model provides a powerful framework for analyzing electrophoretic behavior under various conditions. The calculation formula for the gap G can then be applied to predict and optimize the electrophoretic process, significantly improving efficiency. Figure 5 As shown in Figure E, the system successfully separated CERK1 and CEBiP in approximately 8 minutes at 17.5 V / cm, demonstrating the effectiveness of higher electric field strengths for nucleic acid separation. Therefore, the ET zone diffusion model and gap prediction method have great potential for identifying or separating substances such as nucleic acids and proteins, while also improving electrophoresis efficiency in practical applications.

[0126] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. An electrophoretic separation control method based on an ET zone diffusion model, characterized in that: The steps include: Step 1, establish the ET zone diffusion model; Step 2, setting the running time t and the electric field strength E, and then using the ET zone diffusion model to bring in the running time t and the electric field strength E to calculate the gap G between the two zones; Step 3, judging whether the GE separation is successful based on the size of the gap G. If G is less than zero, it means that the zones overlap and the separation is unsuccessful. If G is greater than zero, it means that the zone separation is successful.

2. The electrophoresis separation control method based on the ET zone diffusion model according to claim 1, characterized in that: In step 1, the established ET zone diffusion model includes the zone migration position model and the bandwidth calculation model; Among them, the migration location model is: In the formula, μ and E represent the electrophoretic mobility and electric field strength of the solution, respectively. Indicates the peak position of the band migration at time point t; The bandwidth calculation model is: In the formula, a, b and c i (i=0,1,…,n) are all constant coefficients of the model.

3. The electrophoretic separation control method based on the ET zone diffusion model according to claim 2, characterized in that: When calculating the three constant coefficients, the calculation formula of the constant coefficient a is: In the formula, σ0 is the initial zone variance; The constant coefficient b is calculated as: In the formula, z and e are the ion valence and electron charge respectively, k represents the Boltzmann constant, and T0 is the ambient temperature; Constant coefficient c i The calculation formula is: In the formula, R is the equivalent resistance of the gel, d is the distance between the positive and negative electrodes, and x i is a constant coefficient.

4. The electrophoresis separation control method based on the ET zone diffusion model according to claim 2, characterized in that: In step 2, the formula for calculating the gap G between two zones is: In the formula, and are the migration positions of the central peaks of the two zones (calculated by the migration position model), and are the bandwidths of the central peaks of the two zones (calculated by the bandwidth calculation model).

5. The electrophoretic separation control method based on the ET zone diffusion model according to claim 2, characterized in that: In step 2, the bandwidth calculation model is optimized according to the zone width approximation effect of the bandwidth calculation model, and the optimized bandwidth calculation model is obtained as follows: In the formula, x0 is a constant coefficient, and the optimized bandwidth calculation model is used as the final bandwidth calculation model.

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