CN112582069A - Neuron dendritic spine development mode establishing method based on reaction diffusion model - Google Patents

Neuron dendritic spine development mode establishing method based on reaction diffusion model Download PDF

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CN112582069A
CN112582069A CN202011573380.XA CN202011573380A CN112582069A CN 112582069 A CN112582069 A CN 112582069A CN 202011573380 A CN202011573380 A CN 202011573380A CN 112582069 A CN112582069 A CN 112582069A
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赵新
贾祎晴
赵启立
孙明竹
郭杉
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Abstract

The invention provides a neuron dendritic spine development mode establishing method based on a reaction diffusion model, which comprises the steps of establishing a dendritic spine shape classification standard according to a rat brain hippocampal neuron dendritic spine shape, simulating the growth process of a single dendritic spine under different conditions by using the reaction diffusion model, classifying simulation results by using the shape classification standard, further simulating the process of growing dendritic spines with different densities under different conditions by using the reaction diffusion model, and further obtaining the neuron dendritic spines with different modes. Compared with the existing research method, the method not only effectively avoids a large number of animal experiments; meanwhile, the reaction diffusion model is applied to the establishment process of the development mode of the dendritic spines of the neurons for the first time, and a foundation is laid for the subsequent research of the pathogenesis of diseases caused by abnormal dendritic spine modes.

Description

Neuron dendritic spine development mode establishing method based on reaction diffusion model
Technical Field
The invention relates to the field of neuron dendritic spine biological patterns, in particular to a neuron dendritic spine development pattern establishing method based on a reaction diffusion model and application of the neuron dendritic spine development pattern establishing method in disease mechanism analysis.
Background
Dendritic spines are minute processes on the dendrites of neurons, widely present in the dendrites of higher animals, and play an important role in the formation of the dendritic synapses of most excitatory axes. Generally dendritic spines are divided into four patterns: elongated, columnar, mushroom, and branched. Wherein, the slender dendritic spines have high plasticity and are related to learning; mushroom-type dendritic spines exhibit poor plasticity and are involved in memory function. Abnormal patterns of dendritic spines are associated with a variety of neurological disorders. For example, there are too many elongated dendritic spines in the somatosensory cortex of fragile X syndrome model mice. The density of dendritic spines in the dendrites of neurons of glioma model mice was significantly reduced. Therefore, it is important to understand the pathogenesis of these diseases and find a therapeutic method by studying the morphology and density of the dendritic spines.
Currently, the main approaches to dendritic spine pattern studies are: the cerebral cortex of the experimental animals and the cerebral cortex of the control animals were compared by brain section. Such studies have major drawbacks: (1) a large number of anatomical animal experiments need to be performed; (2) only one factor influencing the dendritic spine pattern is proposed at a time, and the formation of the dendritic spine is a dynamic process, involves various chemical reactions and is regulated and controlled by various factors.
Therefore, in order to systematically study the mechanism of development of various neurological diseases associated with the dendritic spine patterns, it is necessary to introduce numerical simulation methods to simulate the growth process of the different patterns of dendritic spines.
There are two main types of numerical simulation methods currently used to study the dendritic spine pattern: (1) the volume of dendritic spines is simulated using a brownian motion model, but the brownian motion model describes a random phenomenon, and the pattern formation of dendritic spines is a gene-and environment-regulated process, rather than a random process; (2) the relationship between the forces generated by the cytoskeleton and the deformation of the cell membrane was studied, but this method lacks an explanation for the reason why the cytoskeleton generates different forces. In addition, in the process of carrying out numerical simulation, the method distinguishes different patterns of dendritic spines in a manual identification mode, and subjective errors are inevitably introduced. Therefore, developing a method for establishing a neuron dendritic spine development mode based on a reaction diffusion model, and making morphological classification indexes based on morphological differences of different dendritic spines are very important for researching pathogenesis of diseases caused by abnormal dendritic spine modes.
Disclosure of Invention
The invention provides a method for establishing a neuron dendritic spine development mode based on the defects of the existing mathematical simulation method simulation neuron dendritic spine mode.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for establishing a neuron dendritic spine development mode based on a reaction diffusion model comprises the following steps:
s1, identifying dendritic spines in four modes of mushroom type, column type, long and thin type and branch type in the rat brain hippocampal neuron microscopic image, and measuring the head width w of the dendritic spines in three modes of mushroom type, column type and long and thin typeheadWidth w of neckneckHeight h;
s2, according to the width w of the head of the dendritic spineheadWidth w of neckneckAnd a height h, calculating a relative average width RAW and a relative shrinkage width RCW of the dendritic spines in the three modes in step S1;
s3, establishing classification standards of dendritic spines in different modes;
s4, establishing a reaction diffusion model, setting simulation initial conditions, simulating the growth process of a single dendritic spine by setting variable parameters of the model, applying the classification standard of the step S3 to the reaction diffusion model, and classifying the shape of the dendritic spine in the simulation result;
s5, performing a simulation of a plurality of dendritic spines: and (5) simulating the process of growing a plurality of dendritic spines on a section of dendrite by using the reaction diffusion model in the step S4, and setting variable parameters of the model to obtain different patterns of dendritic spines.
Further, in step S1, the head width w of the dendritic spineheadRefers to the width of the widest part of the dendritic spine away from the dendrites; width w of neckneckRefers to the width of the dendritic spine at its narrowest point in the half near the dendrites.
Further, in step S2, the relative average width RAW of the dendritic spines is calculated as follows:
Figure BDA0002859638250000021
the relative contraction width RCW of the dendritic spines is calculated as follows:
Figure BDA0002859638250000022
wherein, wheadWidth of head of dendritic spine, wneckIs the neck width of the dendritic spine and h is the dendritic spine height.
Further, in step S3, the dendritic spine classification indexes in different patterns are as follows:
(a) branched dendritic spines, if they comprise a branched structure; (b) if the relative average width RAW of the dendritic spines is less than 0.4, the dendritic spines are slender dendritic spines; (c) if the relative average width RAW of the dendritic spines is more than 0.4 and the relative contraction width RCW is less than 0.25, the dendritic spines are columnar dendritic spines; (d) a mushroom-type dendritic spine if the relative average width RAW is greater than 0.4 and the relative shrinkage width RCW is greater than 0.25.
Further, the reaction diffusion models in the steps S4 and S5 are as follows:
Figure BDA0002859638250000031
wherein A, H, S, Y represents the concentration of activator, inhibitor, substrate and cytoskeleton at each point in the simulation region; c is the catalytic rate; μ is the degradation rate of the activator;ρAis the rate of production of the activator; dAIs the diffusion rate of the activator; upsilon is the degradation rate of the inhibitor; rhoHIs the rate of production of the inhibitor; dHIs the diffusion rate of the inhibitor; c. C0A rate of substrate production for the environment; gamma is the degradation rate of the substrate; ε is the rate of substrate consumption; dSIs the diffusion rate of the substrate; e is the degradation rate of the labeling substance; f is a positive feedback coefficient; deltaAIndicates the rate of exogenous activator addition, deltaHIndicating the rate of exogenous inhibitor addition.
Further, in step S4, the simulation initial condition refers to a simulation area size of 100 × 100 pixels, and an area with 10 × 5 pixels disposed in the middle above the area is used as a growth start state of the dendritic spines.
Further, in step S4, the dendritic spine region variable initial state is a ═ 2, H ═ 0.02, S ═ 1, Y ═ 1, the background region variable initial state is a ═ 0.001, H ═ 0.001, S ═ 1, Y ═ 0; at exogenous activator addition rate deltaAExogenous inhibitor addition rate deltaHSubstrate consumption rate, epsilon, as a model variable parameter, and the other parameters were fixed parameters set at c 0.002, μ 0.16, upsilon 0.04, ρA＝0.01，ρH＝0.00005，c0＝0.02，γ＝0.02，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10; the values of the variable parameters of the model are respectively epsilon 0.01-0.90 and deltaA＝0，0.005，0.01，0.015，0.02，δH＝0，0.000025，0.00005，0.000075，0.0001。
Further, in step S5, a dendrite simulation is performed by using a reaction diffusion model, the size of the dendrite simulation area is 150 × 200 pixels, an area with 5 × 10 pixels in the middle of the left side of the area is used as the growth start state of the dendrite, and the values of model parameters are: c is 0.002, μ is 0.16, upsilon is 0.04, ρA＝0.03，ρH＝0.0001，δA＝0，δH＝0，c0＝0.2，γ＝0.02，ε＝0.017，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10; secondly, the first step is to carry out the first,taking the result of the dendritic simulation as the initial condition of the plurality of dendritic spine simulations, carrying out the plurality of dendritic spine growth simulations, and adding the exogenous activator at a rate deltaAExogenous inhibitor addition rate deltaHThe substrate consumption rate epsilon as a model variable parameter, and the other parameters as fixed parameters, c 0.002, μ 0.16, upsilon 0.04, ρA＝0.02，ρH＝0.00005，c0＝0.05，γ＝0.02，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10, and the values of the model variable parameters are respectively 0.5, 1, 1.5, 2, 2.5, and δA＝0，0.01，0.02，0.03，0.04，δH＝0，0.00005，0.0001，0.00015，0.0002。
Furthermore, the method for establishing the development pattern of the neuron dendritic spines can be applied to the analysis and research of pathogenesis of nervous system diseases caused by abnormal dendritic spine patterns.
Compared with the prior art, the invention has the following advantages and effects:
1. according to the method for establishing the neuron dendritic spine development mode, the dendritic spine shape division standard is established through the measurement data of the neuron dendritic spine microscopic image in the hippocampal region of the brain of the rat of the control group, the standard is applied to the reaction diffusion model, and the dendritic spine shapes in the simulation result are automatically classified.
2. According to the method, simulation initial conditions are set according to the actual growth environment of the neuron dendritic spines, the shape of a single dendritic spine and the density of a plurality of dendritic spines are researched by utilizing a reaction diffusion model, and the neuron dendritic spines in different modes are obtained by setting fixed parameters of the model and adjusting variable parameters of the model; meanwhile, the reaction diffusion model is applied to the establishment process of the development mode of the dendritic spines of the neurons for the first time, and a foundation is laid for the subsequent research of the pathogenesis of diseases caused by abnormal dendritic spine modes.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a flowchart of a method for establishing a neuron dendritic spine development pattern based on a reaction diffusion model according to an embodiment of the present invention.
FIG. 2 is a microscopic image (a) of dendritic spines in four shapes on neurons in hippocampal regions of brain of a rat in a control group according to the present invention and a schematic diagram (b) of data to be measured;
FIG. 3 is a diagram of the initial condition setting of the single dendritic spine simulation of the present invention.
FIG. 4 is a diagram of the simulation results of the formation of the dendrite spine shape pattern under different variable model parameter settings according to the present invention.
FIG. 5 is a diagram (a) illustrating initial condition setting of dendrite simulation according to the present invention; a simulation initial condition setting map (b) in which a plurality of dendritic spines are grown on dendrites.
FIG. 6 is a graph of simulation results of formation of dendritic spine density patterns under different variable model parameter settings according to the present invention.
FIG. 7 is a brain hippocampal neuron microscopic image (a) of a control rat according to the present invention; glioma group rat brain hippocampal neuron microscopic image (b); and (c) a glioma rat brain hippocampus neuron dendritic spine mode simulation result graph obtained by utilizing the neuron dendritic spine development mode establishing method disclosed by the invention.
Detailed Description
The present invention will be described in further detail with reference to examples, which are illustrative of the present invention and are not to be construed as being limited thereto.
Example 1: as shown in the flow chart of fig. 1: a method for establishing a neuron dendritic spine development mode based on a reaction diffusion model comprises the following steps:
s1, identificationDendritic spines in four modes of mushroom type, column type, long and thin type and branch type in the microscopic image of the hippocampal neurons of the brain of the other rat are measured, and the head width w of the dendritic spines in the three modes of the mushroom type, the column type and the long and thin type is measuredheadWidth w of neckneckHeight h;
s2, according to the width w of the head of the dendritic spineheadWidth w of neckneckAnd a height h, calculating a relative average width RAW and a relative shrinkage width RCW of the dendritic spines in the three modes in step S1;
s3, establishing classification standards of dendritic spines in different modes;
s4, establishing a reaction diffusion model, setting simulation initial conditions, simulating the growth process of a single dendritic spine by setting variable parameters of the model, applying the classification standard of the step S3 to the reaction diffusion model, and classifying the shape of the dendritic spine in the simulation result;
s5, performing a simulation of a plurality of dendritic spines: and (5) simulating the process of growing a plurality of dendritic spines on a section of dendrite by using the reaction diffusion model in the step S4, and setting variable parameters of the model to obtain different patterns of dendritic spines.
Specifically, in step S1, the neurons used were SD rat hippocampal CA1 region neurons.
The experimental method is as follows: taking out brain tissue, immediately placing the brain tissue into Golgi-Cox staining solution, storing the brain tissue in dark for two weeks, wherein the staining solution is changed every 48 hours, then cutting the brain tissue into brain slices with the thickness of 150 mu m by using a vibratory microtome, placing the brain slices on a 2% gelatin-coated glass slide, staining the brain slices with ammonia water for 60 minutes, washing the brain slices for three times, soaking the brain slices for 30 minutes by using a kodak fixing solution, washing, dehydrating, cleaning, flaking, observing and shooting three-level dendrites of neurons in a hippocampal area of a rat brain under a 100 x objective lens, and finding out 3 mushroom-type dendrites, 3 columnar dendrites, 2 elongated spines and 1 branched dendrite spines in a microscopic image (as shown in figure 2(a), wherein iii, vii and ix represent mushroom types, ii, vi and viii represent columnar types, iv and v represent branched slender spines, and i represents branched spines); the head width of each type of dendritic spine except for the branched type was measured as shown in FIG. 2(b)wheadWidth w of neckneckAnd a height h. Wherein the width w of the head of the dendritic spineheadRefers to the width of the widest part of the dendritic spine away from the dendrites; width w of neckneckRefers to the width of the dendritic spine at its narrowest point in the half near the dendrites.
In step S2, defining a relative average width RAW for measuring the overall width of the dendritic spines, defining a relative contracted width RCW for measuring the difference in width between the head and neck of the dendritic spines, calculating the Relative Average Width (RAW) and the Relative Contracted Width (RCW) using the following formulas;
Figure BDA0002859638250000061
Figure BDA0002859638250000062
according to the measurement result of step S1, the relative average widths RAW of the 3 mushroom-type dendritic spines are calculated to be 0.54, 0.51, 0.65, respectively, and the relative contraction widths RCW are calculated to be 0.38, 0.48, 0.74, respectively; the relative average widths RAW of the 3 columnar dendritic spines are respectively 0.52, 0.96 and 0.93, and the relative contraction widths RCW are respectively 0.09, -0.41 and-0.42; the relative average width RAW of the 2 elongated dendritic spines is 0.30 and 0.32 respectively, and the relative contraction width RCW is 0.16 and 0.30 respectively.
In step S3, the index range corresponding to each dendritic spine shape is divided according to the calculation result in step S2: elongated dendritic spines RAW less than 0.4; the RAW of the columnar dendritic spines is more than 0.4, and the RCW is less than 0.25; mushroom type dendritic spines RAW is greater than 0.4 and RCW is greater than 0.25. From this, a classification criterion for the shape of the dendritic spines can be established: (a) branched dendritic spines, if they comprise a branched structure; (b) if the relative average width RAW of the dendritic spines is less than 0.4, the dendritic spines are slender dendritic spines; (c) if the relative average width RAW of the dendritic spines is more than 0.4 and the relative contraction width RCW is less than 0.25, the dendritic spines are columnar dendritic spines; (d) a mushroom-type dendritic spine if the relative average width RAW is greater than 0.4 and the relative shrinkage width RCW is greater than 0.25.
In steps S4 and S5, the reaction diffusion model used is as follows:
Figure BDA0002859638250000071
a, H, S, Y represents the activator concentration, inhibitor concentration, substrate concentration, and cytoskeleton concentration at each point in the simulated region. Equation (1) is used to calculate the rate of change of the concentration of the activator, and four factors are responsible for the change in the concentration of the activator: autocatalytic, degradative, secretory and diffusive effects of the activator. Equation (2) is used to calculate the rate of change of inhibitor concentration, and there are four factors that cause the change in inhibitor concentration: cross-catalysis, degradation, cellular secretion and diffusion of activators. Equation (3) is used to calculate the rate of change of substrate concentration, and there are four factors that cause the change in substrate concentration: environmental secretion, degradation, depletion of cellular activity and diffusion. Equation (4) is used to calculate the rate of change of the cytoskeleton concentration, and there are three factors that cause the change of the cytoskeleton concentration: cross-catalysis, degradation of the activator and positive feedback with saturation suppression. The parameters in formula (1), formula (2), formula (3) and formula (4) are explained as follows: c is the catalytic rate; μ is the degradation rate of the activator; rhoAIs the rate of production of the activator; dAIs the diffusion rate of the activator; upsilon is the degradation rate of the inhibitor; rhoHIs the rate of production of the inhibitor; dHIs the diffusion rate of the inhibitor; c. C0A rate of substrate production for the environment; gamma is the degradation rate of the substrate; epsilon is the rate at which the cell consumes the substrate; dSIs the diffusion rate of the substrate; e is the degradation rate of the labeling substance; f is a positive feedback coefficient; deltaAIndicates the rate of exogenous activator addition, deltaHIndicates the rate of addition of exogenous inhibitor, delta in the above parametersA、δHEpsilon is a variable parameter of the model, other parameters are fixed parameters of the model, and the substrate consumption rate epsilon and the exogenous activator addition rate delta of the cells are controlled in the simulation processAAnd rate of addition of exogenous inhibitorRate deltaHDifferent patterns of the neuron dendritic spines are obtained.
Specifically, in step S4, the specific method for simulating the growth process of a single dendritic spine is as follows:
as shown in fig. 3, the simulation initial conditions are set, the simulation area size is 100 × 100 pixels, and the area with 10 × 5 pixels in the middle above the area is used as the growth start state of the dendritic spines. The initial state of the dendrite spine region variable is a ═ 2, H ═ 0.02, S ═ 1, Y ═ 1, the initial state of the background region variable is a ═ 0.001, H ═ 0.001, S ═ 1, Y ═ 0; selection of deltaA(rate of exogenous activator addition), deltaH(rate of exogenous inhibitor addition), epsilon (rate of substrate consumption) as model variable parameters, and other parameters were fixed parameters set at c 0.002, μ 0.16, upsilon 0.04, ρA＝0.01，ρH＝0.00005，c0＝0.02，γ＝0.02，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10; the values of the variable parameters of the model are respectively epsilon 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, … …, 0.90 and deltaA＝0，0.005，0.01，0.015，0.02，δ H0, 0.000025, 0.00005, 0.000075, 0.0001, simulation is implemented using C + + language and runs in Visual Studio2015 environment, space step size is 0.3, and all variables are dimensionless quantities. Measuring the width w of the head of the dendritic spine in the simulation resultheadWidth w of neckneckAnd h, calculating the relative average width RAW and the relative shrinkage width RCW of each simulated dendritic spine, and applying the dendritic spine classification standard in the step S3 to classify the simulated dendritic spine, wherein partial simulation results, corresponding indexes and classification results are shown in FIG. 4.
The analysis was as follows: in step S4, by the reaction model variable parameter setting, the influence of the model variable parameter on the shape of the single dendritic spine can be found as follows: as the substrate consumption rate epsilon increases, the dendritic web shape simulation results are mushroom type, column type, long and thin type, and branch type in sequence (as shown in fig. 4 (a)); rate of addition of exogenous activator deltaAPart of the original pattern of elongated dendritic spines is converted into columnar dendritic spines, and part of the original pattern of elongated dendritic spines is converted into columnar dendritic spinesThe dendritic spines whose pattern is columnar are converted into mushroom-type dendritic spines (as shown in fig. 4 (b)); with exogenous inhibitor deltaHThe rate of addition was increased, and part of the dendritic spines, which were originally in a branched form, were converted into elongated dendritic spines (as shown in fig. 4 (c)). Therefore, during the simulation, the parameter δ is varied by the modelA(rate of exogenous activator addition), deltaHThe settings of (exogenous inhibitor adding rate) and epsilon (substrate consumption rate) can realize the conversion between dendritic spines with different shapes.
Specifically, in step S5, the specific method for simulating the growth process of the plurality of dendritic spines is as follows:
firstly, performing dendrite simulation by using a reaction diffusion model, as shown in fig. 5(a), the size of a dendrite simulation area is 150 × 200 pixels, an area with 5 × 10 pixels in the middle of the left side of the area is used as a growth starting state of dendrites, and the values of model parameters are respectively as follows: c is 0.002, μ is 0.16, upsilon is 0.04, ρA＝0.03，ρH＝0.0001，δA＝0，δH＝0，c0＝0.2，γ＝0.02，ε＝0.017，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10;
next, as shown in fig. 5(b), a plurality of dendritic spine growth simulations were performed using the result of the dendritic spine simulation as an initial condition for the plurality of dendritic spine simulations, and δ was selectedA(rate of exogenous activator addition), deltaH(rate of exogenous inhibitor addition), epsilon (rate of substrate consumption) as model variable parameters, and other parameters were fixed parameters set at c 0.002, μ 0.16, upsilon 0.04, ρA＝0.02，ρH＝0.00005，c0＝0.05，γ＝0.02，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10, and the values of the model variable parameters are respectively 0.5, 1, 1.5, 2, 2.5, and δA＝0，0.01，0.02，0.03，0.04，δH＝0，0.00005，0.0001，0.00015，0.0002。
The simulation results are shown in fig. 6, and the analysis shows the following: by setting variable parameters of the reaction model, the variable parameters of the model can be obtained for a plurality of dendritic spinesThe effect of density is: rate of addition of exogenous activator deltaAThe density of dendritic spines is increased in sequence, and the dominant type is changed from a long and thin type to a column type and then to a mushroom type (as shown in figure 6 (a)); with exogenous inhibitor deltaHThe adding rate is increased, the density of the dendritic spines is reduced in sequence, and the dominant type is changed from mushroom type to column type and then to slender type (as shown in fig. 6 (b)); as the substrate consumption rate ∈ increases, the density of dendritic spines decreases in turn, and changes from being predominantly long-length to branched (as shown in fig. 6 (c)). Therefore, during the simulation, the parameter δ is varied by the modelA(rate of exogenous activator addition), deltaHThe setting of (exogenous inhibitor adding rate) and epsilon (substrate consumption rate) can realize the conversion between dendritic spine patterns with different density and shape distribution.
Specifically, as shown in FIG. 6(a), when δH0.00005, ∈ 1; rate of addition of exogenous activator deltaAGradually increasing, part of the dendritic spines with original pattern of slender type is converted into columnar dendritic spines, and part of the dendritic spines with original pattern of columnar type is converted into mushroom type dendritic spines, so that when delta is increasedAWhen the value is 0, a dendrite spine pattern mainly having a long and thin shape is obtained, and when the value is δAWhen the number of the grooves is increased to 0.01, a main columnar dendritic spine pattern is obtained, and when the number of the grooves is increased to deltaAWhen the number of the grooves is increased to 0.04, a mushroom-type main dendritic spine pattern can be obtained.
When delta is shown in FIG. 6(b)A0.01,. epsilon.1, with exogenous inhibitor deltaHThe density of branched dendritic spines gradually decreases with increasing addition rate, therefore, when delta is increasedHWhen δ is 0.00005, a dendrite spine pattern mainly having a long and thin shape can be obtainedHWhen the thickness is increased to 0.0001, the dendritic spine pattern which is all long and thin can be obtained.
When delta is shown in FIG. 6(c)A＝0.01，δHWhen the substrate consumption rate epsilon is increased, the dendritic spine pattern is sequentially changed from a column type to a long and thin type and a branch type, when the epsilon is 1.0, the dendritic spine pattern mainly with the long and thin type can be obtained, and when the epsilon is increased to 2.0, the dendritic spine pattern mainly with the branch type can be obtained.
Further, as shown in fig. 7, the effectiveness of the method is verified by comparing a control group rat and a glioma rat dendritic spine imaging experiment with a glioma rat hippocampal neuron dendritic spine mode simulation graph obtained by using the mode establishing method of the invention.
A group of a plurality of normal SD rats are taken as a control group, a group of a plurality of SD rats suffering from glioma is taken as a glioma group, two groups of rat hippocampal brain slices are prepared, and a dendritic spine pattern on a neuron tertiary dendrite of a rat brain hippocampal area is observed under a microscope. FIGS. 7(a), (b) show microscope images of neuronal dendritic spines in hippocampal regions of normal rats and glioma rats.
The graph (c) is a glioma rat brain hippocampal neuron dendritic spine mode simulation graph obtained by utilizing the mode establishing method of the invention, and the variable parameter delta of the model is obtained at the momentA＝0.01，δH0.0001, ∈ 1, mode fixed parameter c 0.002, μ0.16, ν 0.04, ρA＝0.02，ρH＝0.00005，c0＝0.05，γ＝0.02，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10.
Example 2: the method for establishing the development pattern of the neuron dendritic spines, which is described in the embodiment 1, is applied to the analysis and research of pathogenesis of nervous system diseases caused by abnormal dendritic spine patterns. Compared with the existing research and analysis method, a large number of animal experiments can be avoided.
In addition, it should be noted that the specific embodiments described in the present specification may differ in the shape of the components, the names of the components, and the like. All equivalent or simple changes of the structure, the characteristics and the principle of the invention which are described in the patent conception of the invention are included in the protection scope of the patent of the invention. Various modifications, additions and substitutions for the specific embodiments described may be made by those skilled in the art without departing from the scope of the invention as defined in the accompanying claims.

Claims (9)

1. The method for establishing the development mode of the dendritic spines of the neurons based on the reaction diffusion model is characterized by comprising the following steps of:
s1, identifying dendritic spines in four modes of mushroom type, column type, long and thin type and branch type in the rat brain hippocampal neuron microscopic image, and measuring the head width w of the dendritic spines in three modes of mushroom type, column type and long and thin typeheadWidth w of neckneckHeight h;
s2, according to the width w of the head of the dendritic spineheadWidth w of neckneckAnd a height h, calculating a relative average width RAW and a relative shrinkage width RCW of the dendritic spines in the three modes in step S1;
s3, establishing classification standards of dendritic spines in different modes;
s4, establishing a reaction diffusion model, setting simulation initial conditions, simulating the growth process of a single dendritic spine by setting variable parameters of the model, applying the classification standard of the step S3 to the reaction diffusion model, and classifying the shape of the dendritic spine in the simulation result;
s5, performing a simulation of a plurality of dendritic spines: and (5) simulating the process of growing a plurality of dendritic spines on a section of dendrite by using the reaction diffusion model in the step S4, and setting variable parameters of the model to obtain different patterns of dendritic spines.
2. The method for establishing the development pattern of the dendritic spines of the neuron according to the reaction diffusion model, wherein in the step S1, the head width w of the dendritic spines isheadRefers to the width of the widest part of the dendritic spine away from the dendrites; width w of neckneckRefers to the width of the dendritic spine at its narrowest point in the half near the dendrites.
3. The method for establishing the development pattern of the dendritic spines of the neuron according to the response diffusion model, wherein in the step S2, the relative average width RAW of the dendritic spines is calculated as follows:
Figure FDA0002859638240000011
the relative contraction width RCW of the dendritic spines is calculated as follows:
Figure FDA0002859638240000012
wherein, wheadWidth of head of dendritic spine, wneckIs the neck width of the dendritic spine and h is the dendritic spine height.
4. The method for establishing the development pattern of the neuron dendritic spines based on the reaction diffusion model, according to claim 3, wherein in the step S3, the dendritic spine classification indexes in different patterns are as follows:
(a) branched dendritic spines, if they comprise a branched structure; (b) if the relative average width RAW of the dendritic spines is less than 0.4, the dendritic spines are slender dendritic spines; (c) if the relative average width RAW of the dendritic spines is more than 0.4 and the relative contraction width RCW is less than 0.25, the dendritic spines are columnar dendritic spines; (d) a mushroom-type dendritic spine if the relative average width RAW is greater than 0.4 and the relative shrinkage width RCW is greater than 0.25.
5. The method for establishing the development pattern of the neuron dendritic spines based on the reaction diffusion model according to claim 1, wherein the reaction diffusion models in the steps S4 and S5 are as follows:
Figure FDA0002859638240000021
wherein A, H, S, Y represents the concentration of activator, inhibitor, substrate and cytoskeleton at each point in the simulation region; c is the catalytic rate; μ is the degradation rate of the activator; rhoAIs the rate of production of the activator; dAIs the diffusion rate of the activator; upsilon is the degradation rate of the inhibitor; rhoHIs an inhibitorThe rate of production of; dHIs the diffusion rate of the inhibitor; c. C0A rate of substrate production for the environment; gamma is the degradation rate of the substrate; ε is the rate of substrate consumption; dsIs the diffusion rate of the substrate; e is the degradation rate of the labeling substance; f is a positive feedback coefficient; deltaAIndicates the rate of exogenous activator addition, deltaHIndicating the rate of exogenous inhibitor addition.
6. The method for establishing a development pattern of a neuron dendritic spine according to claim 5, wherein in step S4, the simulation initial condition is that the size of the simulation region is 100 x 100 pixels, and a region with 10 x 5 pixels in the middle above the region is used as the growth starting state of the dendritic spine.
7. The method for establishing the neuron dendritic spine development pattern based on the reaction diffusion model according to claim 6, wherein in step S4, the dendritic spine region variable initial state is a-2, H-0.02, S-1, Y-1, the background region variable initial state is a-0.001, H-0.001, S-1, Y-0; at exogenous activator addition rate deltaAExogenous inhibitor addition rate deltaHSubstrate consumption rate, epsilon, as a model variable parameter, and the other parameters were fixed parameters set at c 0.002, μ 0.16, upsilon 0.04, ρA＝0.01，ρH＝0.00005，c0＝0.02，γ＝0.02，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10; the values of the variable parameters of the model are respectively epsilon 0.01-0.90 and deltaA＝0，0.005，0.01，0.015，0.02，δH＝0，0.000025，0.00005，0.000075，0.0001。
8. The method for establishing a neural dendritic spine development pattern based on the reaction diffusion model as claimed in claim 5, wherein in step S5, a dendritic simulation is first performed using the reaction diffusion model, the size of the dendritic simulation region is 150 x 200 pixels, and a region with 5 x 10 pixels in the middle of the left side of the region is used as the growth start shape of the dendriteThe state and model parameter values are respectively as follows: c is 0.002, μ is 0.16, upsilon is 0.04, ρA＝0.03，ρH＝0.0001，δA＝0，δH＝0，c0＝0.2，γ＝0.02，ε＝0.017，DA＝0.02，DH＝0.26，DS0.06, 0.0035, 0.1, 10; secondly, taking the result of the dendritic simulation as the initial condition of the simulation of the plurality of dendritic spines, carrying out the growth simulation of the plurality of dendritic spines, and adding the exogenous activator at a rate deltaAExogenous inhibitor addition rate deltaHThe substrate consumption rate epsilon as a model variable parameter, and the other parameters as fixed parameters, c 0.002, μ 0.16, upsilon 0.04, ρA＝0.02，ρH＝0.00005，c0＝0.05，γ＝0.02，DA＝0.02，DH0.26, DS 0.06, d 0.0035, e 0.1 and f 10, and the values of the model variable parameters are respectively epsilon 0.5, 1, 1.5, 2, 2.5, delta and deltaA＝0，0.01，0.02，0.03，0.04，δH＝0，0.00005，0.0001，0.00015，0.0002。
9. Use of the method for establishing a developmental pattern of dendritic spines for neurons according to any one of claims 1 to 8 for the study of the analysis of pathogenesis of nervous system diseases caused by abnormal dendritic spine patterns.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106754669A (en) * 2016-11-23 2017-05-31 河海大学常州校区 The preparation method and preparation system of the multi-cellular structure based on Reaction-Diffusion Models
CN110904114A (en) * 2019-12-16 2020-03-24 东北师范大学 Application of Gnb2 gene coding sequence and Gnb2 gene coding sequence in constructing mouse model
CN111465852A (en) * 2017-12-28 2020-07-28 国际商业机器公司 Neural model generation for personalized drug therapy

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106754669A (en) * 2016-11-23 2017-05-31 河海大学常州校区 The preparation method and preparation system of the multi-cellular structure based on Reaction-Diffusion Models
CN111465852A (en) * 2017-12-28 2020-07-28 国际商业机器公司 Neural model generation for personalized drug therapy
CN110904114A (en) * 2019-12-16 2020-03-24 东北师范大学 Application of Gnb2 gene coding sequence and Gnb2 gene coding sequence in constructing mouse model

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
MOHAMMAD NAZRUL ISHLAM PATOARY: "Parallel Stochastic Discrete Event Simulation of Calcium Dynamics in Neuron", 《ACM》 *
郭艺娜: "基于气态反应模型的三维肺分枝形态发生的研究", 《中国优秀博硕士学位论文全文数据库（博士）医药卫生科技辑》 *

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