A model method for calculating distribution difference rate in mitochondrial heterogeneity distribution

Abstract

This invention belongs to the field of biogenetics technology, specifically a data-driven modeling method for calculating the allocation difference rate in mitochondrial heterogeneity distribution. This invention is based on the initial number of mitochondria M in the cell, the initial heterogeneity R0, and the heterogeneity R in the Nth generation. N Distribution difference rate f N Design different mathematical models for the distribution difference rate, that is, design g(·) such that the following equation f N =g(R) N‑1 Establishment: This invention designs a total of 5 types of f N The models include downward parabolic, hyperbolic, slow-then-rapid S-shaped, rapid-then-slow S-shaped, and linear models. Based on the changing trends of clinical time-series data, the corresponding mathematical model for allocation variability is selected to calculate the allocation variability rate in heterogeneous distributions. This invention's method is reasonable and efficient, capable of predicting mitochondrial variation numbers at different generations, thereby guiding clinical medication and treatment.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of biological genetic technology, and particularly relates to a calculation method for distribution difference rate in mitochondrial heterogeneity distribution. BACKGROUND

[0002] Existing researches show that abnormal mitochondria remaining in the nuclear transfer of human nuclear transfer are brought into the donor egg, and a part of the established embryonic stem cell lines has the phenomenon of "genetic drift", in which the originally remaining low mitochondrial DNA increases with the passage of cell generations, and in some cases, even the reverse of the proportion occurs. In particular, human mitochondrial mutations also have a similar "genetic drift" increase phenomenon between generations.

[0003] Researchers have established a "bottle neck model" based on the description of such phenomena. However, the existing model is only a description of the data distribution, and has not given a specific mathematical model and a reasonable explanation. How to start from the data, design a reasonable distribution difference rate mathematical model, and realize the fitting and explanation of the observation data of mitochondrial heterogeneity distribution are key technical problems to be solved. SUMMARY

[0004] The purpose of the application is to provide a reasonable and efficient data-driven calculation method for distribution difference rate in mitochondrial heterogeneity distribution, to predict the number of mitochondrial mutations in different generations, and to guide the clinical medication and treatment.

[0005] The data-driven calculation method for distribution difference rate in mitochondrial heterogeneity distribution provided by the application has the following specific steps:

[0006] (I) Design different distribution difference rate mathematical models

[0007] Let the initial number of mitochondria in the cell be M, the initial heterogeneity rate be R0, that is, the number of normal mitochondria in the initial state is Mx(1-R0), and the number of mutated mitochondria is MxR0; let the heterogeneity rate of the Nth generation (N>0) be R N , and the distribution difference rate be f N .

[0008] The application designs different distribution difference rate mathematical models, that is, designs a reasonable g(·) to make the following formula hold:

[0009] f N =g(R N-1 ), (1)

[0010] Therefore, the number of mutated mitochondria in a cell in the N-1th generation can be calculated as MxR N-1, after one passage, to the Nth generation, the cell is divided into two, one of the cells in the number of variant mitochondria is (the variant mitochondria distribution is more), the other cell in the number of variant mitochondria is (the variant mitochondria distribution is less), and the distribution difference rate is f N , wherein and The distribution difference rate f is calculated by the following formula:

[0011]

[0012] The distribution difference rate mathematical model f N = g(R N-1 ) has the following design principles:

[0013] (1) 0 ≤ f N ≤ 1;

[0014] (2) f N increases with the decrease of R N-1 ;

[0015] (3) when R N-1 = 0, f N = 1; when R N-1 = 1, f N = 0.

[0016] Based on the above model design principles, the present application gives five different g(·) basic mathematical models, and the specific function images are shown in Figure 1 The specific g(·) mathematics is as follows:

[0017] The first model is a downward parabolic type, as shown in Figure 1 (a),

[0018]

[0019] The second model is a hyperbolic type, as shown in Figure 1 (b),

[0020]

[0021] The third model is a slow-quick S type (parabolic-hyperbolic mixed type), as shown in Figure 1 (c),

[0022]

[0023] The fourth model is a quick-slow S type (hyperbolic-parabolic mixed type), as shown in Figure 1 (d),

[0024]

[0025] The fifth model: linear, such as... Figure 1 (e),

[0026] f N =g(R) N-1 )=1-R N-1 , 0≤R N-1 ≤1. (7).

[0027] (II) Data-driven model selection rules:

[0028] Based on clinical time-series data, calculations were performed on the data at different discrete time points. Discrete derivative values ​​on (i.e., the difference form of the derivative): Different models are selected based on the trend of the derivative. Specifically, the following five rules are followed:

[0029] ① If the absolute value of the derivative (which can be negative) gradually increases, then choose Model 1 (clinical data show that the allocation difference rate decreases as the heterogeneity rate of the previous generation decreases, and the rate of decrease increases as the heterogeneity rate of the previous generation increases).

[0030] ② If the absolute value of the derivative (which can be negative) gradually decreases, then choose Model 2 (clinical data show that the rate of allocation variability decreases as the rate of decrease of heterogeneity in the previous generation increases).

[0031] ③ If the absolute value of the derivative (which can be negative) first gradually increases and then gradually decreases, then choose Model 3 (clinical data show that the rate of allocation variability increases and then decreases as the rate of decrease of heterogeneity in the previous generation increases as the rate of heterogeneity in the previous generation increases).

[0032] ④ If the absolute value of the derivative (which can be negative) first gradually decreases and then gradually increases, then choose Model 4 (clinical data show that the rate of decrease in the heterogeneity rate of the previous generation first decreases and then increases as the heterogeneity rate of the previous generation increases).

[0033] ⑤ If the absolute value of the derivative (which can be negative) remains unchanged, then select Model 5 (clinical data show that the rate of allocation variability decreases with the heterogeneity rate of the previous generation, but the rate remains unchanged).

[0034] Model selection criteria: Based on clinical sequence data performance, calculations... And judge Follow Based on the changing trend, select the appropriate model by choosing a rule that aligns with that trend, for example... Follow The overall trend of change is that the absolute value gradually decreases, which satisfies rule ②, so model 2 is selected.

[0035] Based on the different mathematical models, the number of different generations of mitochondria in cells is obtained based on clinical experiments, and the application can realize the fitting and interpretation of the observation data of mitochondrial heterogeneity distribution according to the completely data-driven selection allocation difference rate mathematical model, and meet the following three characteristics: (1) bidirectional chemotaxis; (2) skew polarization, and (3) polarization aggravates in a trap type with the increase of skew.

[0036] The application can use the mathematical model designed based on clinical data, and independently select a suitable fitting model according to the characteristics of clinical data to predict the number of different generations of mitochondria, and guide the clinical medication and treatment. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is the allocation difference rate mathematical model. Wherein, (a) the first model; (b) the second model; (c) the third model; (d) the fourth model; (e) the fifth model. DETAILED DESCRIPTION

[0038] The method of the application will be further described below through examples.

[0039] For clinical data showing that the allocation difference rate decreases with the heterogeneity rate of the previous generation, it is assumed that the absolute value of the discrete derivative on different time points decreases gradually, that is, the decreasing rate decreases with the increase of the heterogeneity rate of the previous generation, and based on such data trend, the application will independently select the second model, specifically:

[0040] The function formula of the second model is Its derivative is:

[0041]

[0042] The absolute value of which is will decrease with the increase of R N-1 , and presents the same trend as the calculated of the clinical data, based on rule ②, the application will independently select the second model;

[0043] Therefore, according to formula (2), the variation rate of the Nth generation can be calculated as:

[0044]

[0045] Specifically, assuming that R0=25%, the calculation formula of the application can obtain:

[0046] At the first generation, At the second generation, and ​Thus, the mitochondrial mutation rate of any Nth generation can be calculated, and the precise model fitting of clinical mitochondrial data can be achieved.

Claims

1. A data driven modelled approach to the calculation of allocation disparity rates in mitochondrial heteroplasmy distribution, characterized in that, The specific steps are as follows: (I) design different allocation difference rate mathematical models Let the initial number of mitochondria in the cell be M, and the initial heterogeneity rate be R0, i.e. the number of normal mitochondria in the initial state is M x (1-R0), and the number of variant mitochondria is M x R0; let the heterogeneity rate of the Nth generation be R N , and the distribution difference rate be f N ; Design a reasonable function g(·) so that the following formula is true: f N = g(R N-1 ), (1) Let the number of variant mitochondria in a certain cell of the N-1th generation be M x R N-1 After one passage, the cell is divided into two, one of which has a number of variant mitochondria of The variant mitochondria are distributed more; the other cell has a number of variant mitochondria of The variant mitochondria are distributed less; the difference rate of distribution is f N Then And are calculated by the following formula: Mathematical model of the allocation variance rate f N = g(R N-1 ) is as follows: (1)0≤f N ≤1； (2)f N With decreasing R N-1 increasing. (3) R N-1 = 0, f N = 1; R N-1 = 1, f N = 0, Based on the above design principles, five different g(·) basic mathematical models are given as follows: Model 1: 2nd model: The third model: The fourth model: Model 5: f N = g(R N-1 ) = 1 - R N-1 , 0 < R N-1 < 1, (7) (ii) Data-driven model selection rule: Based on the clinical time series data, the derivative of the data at different discrete time points x k is calculated, and different models are selected based on the trend of the derivative; specifically: If the absolute value of the derivative gradually increases, the first model is selected, and the clinical data shows that the allocation difference rate decreases with the heterogeneity rate of the previous generation, and the rate of decrease increases with the increase of the heterogeneity rate of the previous generation; If the absolute value of the derivative gradually decreases, the second model is selected, and the clinical data shows that the rate of decrease of the allocation difference rate with the heterogeneity rate of the previous generation decreases with the increase of the heterogeneity rate of the previous generation; If the absolute value of the derivative gradually increases and then gradually decreases, the third model is selected, and the clinical data shows that the rate of decrease of the allocation difference rate with the heterogeneity rate of the previous generation first increases and then decreases with the increase of the heterogeneity rate of the previous generation; If the absolute value of the derivative first gradually decreases and then gradually increases, the fourth model is selected, and the clinical data shows that the rate of decrease of the allocation difference rate with the heterogeneity rate of the previous generation first decreases and then increases with the increase of the heterogeneity rate of the previous generation; If the absolute value of the derivative remains unchanged, the fifth model is selected, and the clinical data shows that the allocation difference rate decreases with the heterogeneity rate of the previous generation, but the rate remains unchanged.

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