Method for constructing biological heterogeneity neural network

Abstract

The invention provides a method for constructing a biological heterogeneity neural network. The method comprises the following steps: S1, on the basis of an ion channel function abstraction method, taking a constant in an activation gate and deactivation gate dynamic function of an ion channel in a first dimension raising model as an undetermined dynamic coefficient P (theta); s2, optimizing ion channels corresponding to the second dimension raising model based on the number of the ion channels of the target model; s3, searching all undetermined coefficients P (theta) and corresponding conductance values G in the second dimension raising model ion channel kinetic equation based on a random parameter search method to obtain solutions to be selected; S4, processing a target model based on polar coordinate projection to obtain a degeneracy characteristic model between ion channel currents; s5, performing minimum mean square error calibration on all to-be-selected solutions in the second dimension raising model to obtain a third dimension raising model; s6, on the basis of polar coordinate projection, taking each current intersection point in the third dimension raising model as a degeneracy feature, screening a to-be-selected solution which is most similar to the degeneracy feature model between the ion channel currents as an optimal solution, and constructing a biological heterogeneity neural network; according to the method, model parameters and structures which more accord with biological reality can be obtained through high-degree-of-freedom ion channel kinetic parameter random search in combination with non-time-scale inter-channel degeneracy comparison.

Description

Technical Field

[0001] The present invention relates to the neuron model simulation technology in the field of computational neuroscience, and particularly to a method for constructing a biologically heterogeneous neuron network. Background Art

[0002] A neuron model is a digital tool that quantitatively describes the electrophysiological characteristics of biological neurons through mathematical equations and computational algorithms. Its core components include the dynamic equation of the cell membrane potential, the conduction mechanism of ion channels, and the synaptic information transmission rule, etc.

[0003] In the field of computational neuroscience, the neuron model, as the basic unit for studying neural information processing, has important application values in aspects such as the development of brain-computer interfaces, the research on the mechanisms of nervous system diseases, and the construction of brain-like intelligent systems. Existing neuron models are mainly divided into two categories: biophysical models (such as the Hodgkin-Huxley model) and simplified computational models (such as the Integrate-and-Fire model). The former aims at simulation, and many types of models have been developed to simulate the action potentials of neurons with different organisms and different characteristics, and almost all of them use the Hodgkin-Huxley model and its differential equations of ion channels as the basic framework. Although these models can well restore the characteristics of various electrical activities (such as specific discharge frequencies, specific maximum / minimum voltage values, subthreshold potentials, burst discharges, etc.), the correlation coefficients of the conductance values of their respective channels deviate from the biologically measured data, seriously affecting the biological credibility of the models. The sources of this error may be twofold: one is that the number of dimensions of the model is insufficient, and the number of ion channels in the model does not match the actual situation, resulting in some channels of the same type being represented in a reduced dimension, affecting the correlation coefficient between channels; the other is that although the model can generate the target action potential, there are deviations between the kinetic parameters of its ion channels and the actual parameters. In addition, in biological neural networks, neurons exhibit significant heterogeneity, such as the diversity of ion channel types and numbers, and the differences in electrophysiological characteristics, etc. However, existing neuron models usually assume that neurons are homogeneous units, and it is difficult to accurately simulate the complex behaviors of heterogeneous neural networks, which poses new challenges for constructing biologically credible neuron networks. Summary of the Invention

[0004] Aiming at the problems of existing models, the present invention provides a method for constructing a biologically heterogeneous neural network to address the deficiencies in biological plausibility and non - heterogeneity of existing models. By means of a high - degree - of - freedom ion channel kinetics parameter - searching process and a novel measurement of inter - channel degeneracy, model parameters are screened. Here, degeneracy refers to the fact that the currents of different ion channels may exhibit similar behaviors under specific conditions, that is, combinations of multiple ion channels can produce the same electrophysiological characteristics. This phenomenon is prevalent in biological neurons, reflecting the functional redundancy and diversity among ion channels, and is an important source of the complexity and robustness of biological neural networks. This method can, while retaining the action potential characteristics of the target model, provide biologically realistic inter - channel conductance correlation coefficients and simulate the electrophysiological characteristics of heterogeneous neurons, thus providing a new method for constructing a biologically plausible heterogeneous neural network.

[0005] To solve the problems of the existing technology, the present invention adopts the following technical solutions:

[0006] A method for constructing a biologically heterogeneous neural network, the method being based on a neural network, a first dimensionality - raising model, a second dimensionality - raising model, a third dimensionality - raising model, and a target model, and comprising the following steps:

[0007] S1. Based on the ion - channel function abstraction method, the constants in the activation - gate and inactivation - gate kinetic functions of the ion channels in the first dimensionality - raising model are taken as undetermined kinetic coefficients P(Θ), that is:;

[0008] α n = f1(V, P(Θ1)), β n = f2(V, P(Θ2))

[0009] α n = θ1*(V + θ2) / (1 - exp(-(V + θ2) / θ3), θ1, θ2, θ3 ∈ P(Θ1)

[0010] β n = θ4*exp(-(V + θ5) / θ6), θ4, θ5, θ6 ∈ P(Θ2)

[0011] where P(Θ) represents the undetermined coefficients in the ion - channel kinetic equation;

[0012] S2. The first dimensionality - raising model constructs a second dimensionality - raising model with a matching number of ion channels according to the number of each ion channel in the target model, and respectively constructs independent undetermined kinetic coefficients P(Θ) and corresponding conductance values G for the ion channels in the second dimensionality - raising model;

[0013] S3. Search for all undetermined coefficients \(P(\Theta)\) and corresponding conductance values \(G\) in the ion channel kinetic equation of the second upscaled model based on the random parameter search method. If the undetermined kinetic coefficient \(P(\Theta)\) and the corresponding conductance value \(G\) during a certain search process are within the confidence interval of the corresponding characteristics of the target model in the second upscaled model, then take the undetermined kinetic coefficient \(P(\Theta)\) and the corresponding conductance value \(G\) as a group of candidate solutions;

[0014] S4. Process the ion channel currents of the target model based on polar coordinate projection to obtain a degeneracy characteristic model between ion channel currents;

[0015] S5. Calibrate the ion channel currents of all candidate solutions in the second upscaled model according to the minimum mean square error between current curves to obtain a third upscaled model;

[0016] S6. Based on polar coordinate projection, take the current intersection points in the third upscaled model as degeneracy characteristics, and screen the candidate solution most similar to the degeneracy characteristic model between ion channel currents as the optimal solution, and then construct a biological heterogeneity neuron network.

[0017] Further, in step S4, processing the ion channel currents of the target model based on polar coordinate projection to obtain a degeneracy characteristic model between ion channel currents includes:

[0018] Decompose multiple action potentials within a continuous time window into a combination of multiple single discharges, and record the start sequence value and end sequence value of each single discharge;

[0019] Decompose each channel current into multiple groups according to the start sequence value and end sequence value, and use linear interpolation to divide each group of currents into an integer multiple of \(2\pi\) parts with a precision greater than the minimum time step;

[0020] Process the absolute value of each group of current data using the natural logarithm, and add a constant bias \(C\);

[0021] I log =\(\log(\vert I\vert+\max\{\vert I\vert,0\}+C)\)

[0022] where \(I\) log is the processed current data, and \(I\) is the current data between the start sequence value and end sequence value of a certain group;

[0023] By mapping \(I\) log to the polar coordinates in the angular range of \((0, 2\pi)\);

[0024] I log =[I1, I2, …, I N

[0025] ​

[0026] Among them, I log is the processed current data, with a length of N. n is the index of the current current point, and n ∈ [1, N]; r n is the distance in polar coordinates, and θ n is the angle in polar coordinates; I n is the value of the current current point; for the entire current data I log , its polar coordinate mapping can be expressed as:

[0027]

[0028] Furthermore, in the step S5, the ion channel currents of all candidate solutions in the second dimensionality-raising model are calibrated according to the minimum mean square error between current curves to obtain a third dimensionality-raising model; where:

[0029] The formula for the minimum mean square error is as follows:

[0030]

[0031] I1 = [I1 (1) , I1 (2) , I1 (3) ,... I1 (n) , I2 = [I2 (1) , I2 (2) , I2 (3) ,... I2 (n)

[0032] Among them, I1 (i) represents the current value of the i-th point in the first current sequence, and I2 (i) represents the current value of the i-th point in the second current sequence, and n represents the length of the current sequence.

[0033] Beneficial effects

[0034] Compared with the traditional technical solution, the beneficial effects brought by the present invention are:

[0035] The present invention proposes a method for constructing a complex model neural network with heterogeneity based on a dimensionality-raising Hodgkin-Huxley model. Compared with general neuron biophysical models, this method can obtain model parameters and structures that are more in line with biological reality through random search of high-degree-of-freedom ion channel kinetic parameters and comparison of channel degeneracy without time scale, and can effectively improve the biological credibility of the model. Description of the drawings

[0036] Figure 1 : Degeneracy diagram between potassium ion and sodium ion channels of the H-H model under polar coordinate projection;​

[0037] Figure 2 : Comparison of the degeneracy of the ion channels corresponding to the 9 candidate solutions with the target model (C-S model) (marked as the most similar group);

[0038] Figure 3 : Correlation coefficient of the channel conductance of the target model (C-S model) and the correlation coefficient under the optimal solution; Detailed implementation manners

[0039] The following further describes the technical solutions of the present invention in conjunction with the appended Figure 1 - appended Figure 3 drawings,

[0040] In view of the deficiencies that the correlation coefficient between the ion channels of the existing model does not conform to the biological reality and the biological credibility is poor, the present invention provides a method for constructing a biologically heterogeneous neuron network. The method is based on a neuron network, a first dimensionality-increasing model, a second dimensionality-increasing model, a third dimensionality-increasing model, and a target model, and includes the following steps:

[0041] S1. For the abstraction of the ion channel function, the present invention takes the constants in the activation gate and inactivation gate kinetic functions of the potassium ion, sodium ion and other channels of the first dimensionality-increasing model as undetermined coefficients P(Θ), and abstracts the overall differential equation without changing the framework of its ordinary differential equation, liberating the degree of freedom of the ion channel kinetic equation to the greatest extent, so that on the basis of the first dimensionality-increasing model, the action potential characteristics of as complex a model as possible can be simulated to obtain the second dimensionality-increasing model. Among them: the detailed analysis process of the ion channel function abstraction:

[0042] The ion channel function abstraction is achieved by setting all the constants in the ordinary differential kinetic equations of each ion channel of the normal first dimensionality-increasing model as undetermined parameters. Taking the potassium ion channel as an example:

[0043] α n = 0.01*(V + 55) / (1 - exp(-(V + 55) / 10))

[0044] β n = 0.125*exp(-(V + 65) / 80)

[0045]

[0046] I K = g K *n 4 *(V - E K )

[0047] Among them: n represents the activation gate of the potassium ion channel, α n and β nDetermine the updated state of the potassium ion channel activation gate at each time step. V represents the membrane voltage value of the previous state, and E K represents the potassium ion reversal potential, and g K represents the conductance value corresponding to the potassium ion channel. The potassium ion channel contains an activation gate n, which is determined by α n and β n to determine the updated state, and combines the activation gate state of the previous moment to determine the activation gate state of the current moment. The potassium ion current at the current moment is determined by four variables: the potassium ion channel conductance value, the current activation gate state, and the current membrane voltage value. Set all the constant terms among them as undetermined coefficients:

[0048] α n = f1(V, P(Θ1)), β n = f2(V, P(Θ2))

[0049] α n = θ1*(V + θ2) / (1 - exp(-(V + θ2) / θ3)), θ1, θ2, θ3 ∈ P(Θ1)

[0050] β n = θ4*exp(-(V + θ5) / θ6), θ4, θ5, θ6 ∈ P(Θ2)

[0051] where P(Θ) represents the undetermined coefficients in the ion channel kinetic equation. The solution of this ordinary differential equation is obtained from the inputs required by the original H-H model: the initial value of the membrane voltage V, the initial value of the potassium ion channel activation gate n, the initial value of α n , the initial value of β n , the potassium ion channel conductance value g K , and the potassium ion reversal potential E K parameter values, and becomes that it is also necessary to additionally input the P(Θ) of α n and β n respectively.

[0052] S2. Referring to the number of each ion channel in the target model, dimension up the corresponding ion channels of the second dimension-up model so that each ion channel of the target model can be corresponding one by one, ensuring that it has a similar complexity to the target model to achieve various characteristics of the action potential. At this time, the kinetic equations and conductance values among the ion channels in the second dimension-up model are independent of each other.

[0053] It is necessary to process the abstracted second dimension-up model according to the number of each ion channel in the target model. For example: compared with the H-H model, the Connor-Steven model (hereinafter referred to as the C-S model) contains two potassium ion channels g KDR and g A , then it is necessary to dimension up the potassium ion channel g K of the H-H model to gK1 , g K2 to match the complexity of the C-S model:

[0054] α n1 = A1 * (V + B1) / (1 - exp(-(V + B1) / C1))

[0055] α n2 = A2 * (V + B2) / (1 - exp(-(V + B2) C2), A1, A2, B1, B2, C1, C2 ∈ P(Θ1)

[0056] β n1 = D1 * exp(-(V + E1) / F1)

[0057] β n2 = D2 * exp(-(V + E2) / F2), D1, D2, E1, E2, F1, F2 ∈ P(Θ2)

[0058]

[0059] I K = (V - E K ) * (g K1 * n1 4 + g K2 * n2 4 )

[0060] This lays the foundation for the subsequent random parameter search process.

[0061] S3. Constrained by the action potential characteristics of the target model at the reference parameter values, a random parameter search process is used to search for all undetermined coefficients P(Θ) and corresponding conductance values G in the ion channel kinetic equation of the second dimensionality - up model. If the P(Θ) and G in a certain search process make the action potential characteristics of the second dimensionality - up model conform to the confidence interval of the corresponding characteristics of the target model, then this set of P(Θ) and G is taken as a set of candidate solutions. Among them: the random parameter search

[0062] Constrained by the action potential characteristics of the target model at the reference parameter values, a random parameter search process is used to search for all undetermined coefficients P(Θ) and corresponding conductance values G in the ion channel kinetic equation of the H - H model. If the P(Θ) and G in a certain search process make the action potential characteristics of the H - H model conform to the confidence interval of the corresponding characteristics of the target model, then this set of P(Θ) and G is taken as a set of candidate solutions.

[0063] Random parameter search needs to use the features of the target model under the reference parameter values as the criteria to guide the screening of candidate solutions. First, determine a sufficiently large number of iterations to generate several groups of random P(Θ) and the conductance values G of each channel. For each group of randomly generated parameters, extract the features of the action potential obtained after inputting them into the dimensionality-increased H-H model.

[0064] Taking the C-S model as an example, the features that need to be extracted from its action potential are: discharge frequency, maximum membrane voltage, minimum membrane voltage, length of subthreshold potential, depolarization length, repolarization length, etc.; these features are extracted by methods that conform to general definitions. For example, the maximum / minimum value of the membrane voltage is obtained by taking all the maximum / minimum values greater than a certain threshold after the action potential reaches a steady state and averaging them. The adjacent maximum / minimum values can be regarded as a complete spike potential; the discharge frequency is obtained by determining that the number of maximum values is greater than the expected value, that is, when the model is in a periodic discharge state, taking the difference between the indexes of two adjacent extreme values multiplied by the time step and then taking the reciprocal; the length of the subthreshold potential and the depolarization length are based on the rising branch in each complete spike potential. Taking the mean value of the interval from the current peak to 1 / 3 before the next peak as the threshold, the voltage interval rising branch below this threshold is used as the subthreshold part, and the rising branch above this threshold is used as the depolarization part, and the lengths of the two parts are calculated respectively.

[0065] The repolarization length is the length of the falling branch. The above operations are used to obtain the reference range of the constraint conditions on the standard C-S model and to judge the characteristics of the third-dimensionality-increased model at the current solution during the random parameter search process.

[0066] After a sufficient number of iterations, a certain number of candidate solutions that meet the constraint conditions will be obtained. The parameters represented by these solutions can make the second-dimensionality-increased model generate action potential characteristics that meet the constraint conditions.

[0067] S4. Perform polar coordinate projection on the ion channel currents of the target model. Using the two adjacent voltage minimum values of a single spike potential as the starting index and the ending index, group the current data of each ion channel according to the starting index and the ending index, and use linear interpolation to divide each group of currents into integer multiples of 2π with a precision greater than the minimum time step. After taking the absolute value, taking the natural logarithm, and bias processing of the current values, use the processed current values as the radius and the relative index position of the current point as the angle, and project them onto the polar coordinates in the range of [0, 2π] to obtain a degeneracy model of ion channel currents on a non-time scale.

[0068] S5. Obtain the third-dimensionality-increased model for the ion channel currents of the candidate solutions in the second-dimensionality-increased model according to the minimum mean square error between the corresponding current curves.

[0069] S6. Based on polar coordinate projection, taking each current intersection point in the third dimensionality elevation as a degeneracy feature, screening out the candidate solution most similar to the degeneracy model between the ion channel currents of non-time scales as the optimal solution, and finally obtaining a dimensionality elevation model with the ion channel conductance correlation coefficient conforming to biological reality, providing a model parameter basis for a heterogeneous neural network with high biological credibility. The process of polar coordinate projection and degeneracy comparison:

[0070] To obtain the optimal solution from the candidate solutions, it is necessary to further project each ion channel current onto the polar coordinates for comparison of inter-channel degeneracy.

[0071] First, determine the range of each projection: Take the indices of two adjacent lowest voltage points in the action potential, i.e., the starting index and the ending index, as the range of a single spike potential. At this time, the product of its index and the time step represents the time of each voltage point, and its value represents the membrane voltage value at the corresponding time. Also split the current sequences of all ion channels according to the starting index and the ending index, and then use linear interpolation to split each group of currents into an integer multiple of 2π with a precision greater than the minimum time step. That is, if the time step is 0.01 s, and the difference between the starting index and the ending index is about 1000, then it is necessary to use linear interpolation to amplify the current sequence to a length of 360(2π)*3 = 1080, so as to project it onto the polar coordinates.

[0072] Second, it is necessary to take the absolute value, natural logarithm processing and bias processing (such as adding a constant 1 to all processed current values) of the current sequence to minimize the influence of the conductance value on the inter-channel degeneracy. Take the processed current value as the radius and the relative index position of the current point as the angle, and project it onto the polar coordinates in the range of [0, 2π] to obtain the degeneracy situation between the ion channel currents of non-time scales:

[0073]

[0074] where I is the processed current data, with a length of N, n is the index of the current point, n ∈ [1, N]; r n is the distance (radius) in the polar coordinates, θ n is the angle in the polar coordinates; I n is the value of the current point. For the C-S model and the normal H-H model, the polar coordinate projections of their currents are as Figure 1 shown.

[0075] Figure 1 The degeneracy between the ion channel currents shown is visually manifested, and at the same time, the influence of the conductance value change and the time axis is eliminated as much as possible.

[0076] Finally, for all candidate solutions, select the solution with the lowest total mean square error between the corresponding current curves of the target model and the highest degeneracy similarity of the current intersection points within the model as the optimal solution. The specific quantity depends on the degree of heterogeneity required by the neural network. The formula for calculating the minimum mean square error is as follows:

[0077]

[0078] I1 = [I1 (1) , I1 (2) , I1 (3) ,... I1 (n) , I2 = [I2 (1) , I2 (2) , I2 (3) ,... I2 (n)

[0079] Among them, I1 (i) represents the current value at the i-th point in the first current sequence, and I2 (i) represents the current value at the i-th point in the second current sequence. n represents the length of the current sequence (the lengths of the two sequences are the same). Figure 2 Shown are the polar coordinate projections of the nine optimal solutions with the smallest minimum mean square error between the current curves among a sufficient number of candidate solutions.

[0080] Figure 2 Shows the current polar coordinate situation of the C-S model (upper left figure) and the current polar coordinate degeneracy situation of 9 groups of optimal solutions. Figure 2 For a group of optimal solutions circled in, the intersections between the currents in its current polar coordinates are most similar to the C-S model. See Figure 3 for the specific ion channel correlation coefficients under this group of solutions.

[0081] Figure 3 Shows that compared with the C-S model (upper figure), the conductance correlation coefficients between channels of the dimensionality-increased H-H model (lower figure) under the optimal solution are significantly more in line with biological reality (experimental data show that the expression levels of various ion channels in real neurons do not show negative correlations).

[0082] Although the present invention has been described above, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many variations without departing from the gist of the present invention, and these all fall within the protection scope of the present invention.​

Claims

1. A method for constructing a biologically heterogeneous neuron network, characterized in that: The method is based on a neural network, a first dimension-raising model, a second dimension-raising model, a third dimension-raising model, and a target model, and includes the following steps: S1. Based on the ion channel function abstraction method, the constants in the activation gate and inactivation gate kinetic functions of the ion channels in the first dimension-raising model are used as undetermined kinetic coefficients P(Θ), that is:; α n = f1(V, P(Θ1)), β n = f2(V, P(Θ2)) α n = θ1 * (V + θ2) / (1 - exp(-(V + θ2) / θ3)), where θ1, θ2, θ3 ∈ P(Θ1) β n = θ4*exp(-(V + θ5) / θ6), where θ4, θ5, θ6 ∈ P(Θ2) where P(Θ) represents the undetermined coefficients in the ion channel kinetic equation; S2. The first dimension-raising model constructs a second dimension-raising model with a matching number of ion channels according to the number of ion channels in the target model, and constructs independent undetermined kinetic coefficients P(Θ) and corresponding conductance values G for the ion channels in the second dimension-raising model respectively; S3. Based on the random parameter search method, all undetermined coefficients P(Θ) and corresponding conductance values G in the ion channel kinetic equation of the second dimension-raising model are searched. If the undetermined kinetic coefficients P(Θ) and corresponding conductance values G in a certain search process are within the confidence interval where the characteristics of the second dimension-raising model match the corresponding characteristics of the target model, then the undetermined kinetic coefficients P(Θ) and corresponding conductance values G are used as a set of candidate solutions; S4. Based on polar coordinate projection, the ion channel currents of the target model are processed to obtain a degeneracy characteristic model between ion channel currents; S5. The ion channel currents of all candidate solutions in the second dimension-raising model are calibrated according to the minimum mean square error between current curves to obtain a third dimension-raising model; S6. Based on polar coordinate projection, the current intersection points in the third dimension-raising model are used as degeneracy characteristics, and the candidate solution most similar to the degeneracy characteristic model between ion channel currents is selected as the optimal solution, and then a biological heterogeneity neural network is constructed.

2. The method for constructing a bio-heterogeneous neuron network according to claim 1, characterized in that: In the S4 step, based on polar coordinate projection, the ion channel currents of the target model are processed to obtain a degeneracy characteristic model between ion channel currents; it includes: Decompose multiple action potentials in a continuous time window into a combination of multiple single discharges, and record the start sequence value and end sequence value of each single discharge; Decompose each channel current into multiple groups according to the start sequence value and end sequence value, and use linear interpolation to divide each group of currents into an integer multiple of 2π with a precision greater than the minimum time step; Process the absolute value of each group of current data with natural logarithm and add a constant bias C; I log = log(abs(I) + max{abs(I), 0} + C) Among them, I log is the processed current data, and I is the current data between a certain set of start sequence values and end sequence values; By mapping I log onto polar coordinates in the angular range of (0, 2π); I log = [I1, I2, …, I N ​ Among them, I log is the processed current data with a length of N, n is the index of the current current point, and n ∈ [1, N]; r n is the distance in polar coordinates, and θ n is the angle in polar coordinates; I n is the value of the current current point; for the entire current data I log , its polar coordinate mapping can be expressed as:

3. The method for constructing a heterogeneous biological neuron network according to claim 1, characterized in that: In the S5 step, the ion channel currents of all candidate solutions in the second dimension-raising model are calibrated according to the minimum mean square error between current curves to obtain a third dimension-raising model; where: The calculation formula for the minimum mean square error is as follows: I1 = [I1 (1) , I1 (2) , I1 (3) ,... I1 (n) , I2 = [I2 (1) , I2 (2) , I2 (3) ,... I2 (n) ​ Among them, I1 (i) represents the current value of the i-th point in the first current sequence, I2 (i) represents the current value of the i-th point in the second current sequence, and n represents the length of the current sequence.

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