Construction method of digital twin zebrafish nervous system based on calcium wave imaging signals

Abstract

The present invention provides a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals: Step 1, estimate the probability distribution of neuron connections between different brain regions of zebrafish based on experimental data, and generate a network connection structure. Step 2, calculate the neuron excitation and inhibition indicators based on the calcium wave imaging signals of zebrafish to obtain neuron type information. Step 3, construct a zebrafish neural network model based on the connection data and neuron type information, and delimit the parameters to be assimilated. Step 4, use ensemble Kalman filtering to assimilate the parameters to be assimilated until the correlation between the calcium wave data generated by the system and the experimental data is high enough. Step 5, perform simulation tests using the assimilated system parameters. If the correlation between the calcium wave signals generated by the system and the experimental data is weak, repeat Step 4 until the conditions in Step 4 are met. Step 6, use the iteratively assimilated parameters as the system parameters to complete the construction of the zebrafish neuron system.

Description

Technical Field

[0001] The present invention relates to the technical field of brain science research, and particularly relates to a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals. Background Art

[0002] Data assimilation algorithms are widely used in inverse problems such as estimating system parameters, for example, constructing a digital twin system of a biological neural network based on observed signals. However, when it comes to the situation where the signal granularity reaches the single neuron level and the number of neurons is large, these methods have a high complexity and are difficult to directly implement. When the understanding of the model structure of the system is limited and the sampling frequency of the observed signal itself is low, the challenges faced by assimilation are even greater.

[0003] The model animal zebrafish has nearly one hundred thousand neurons. Currently, only the calcium wave sequences of some of its neurons can be observed, and there is insufficient understanding of the precise connection structure of neurons, various neuron types, and the modeling and analysis of other unobserved neurons. Moreover, the sampling frequency of the obtained calcium wave sequences is low, which makes it difficult to solve inverse problems such as inferring system parameters.

[0004] Based on experimental data and kinetic analysis, various mathematical models of neurons have been proposed, ranging from relatively simple integrate-and-fire models to relatively complex multi-compartment models. Although more complex neuron models can better reflect real neural activities, their complexity leads to extremely low efficiency in large-scale simulations, and their large parameter space brings huge computational costs to data assimilation. In addition, there is also uncertainty in the current modeling of the mechanism of calcium wave generation by zebrafish neuron discharges, which brings further difficulties to assimilation. Moreover, there is also a large uncertainty in the modeling of the influence of dopamine-modulated neurons lacking observed data on the system.

[0005] Reconstructing the entire nervous system model based on the calcium signals of some zebrafish neurons also poses a great challenge to existing assimilation algorithms. Due to the nonlinearity of the model, the Ensemble Kalman Filter (EnKF) is generally selected as the data assimilation algorithm. However, at this time, the computational complexity of EnKF is high (cubic relationship with the number of neurons and the dimension of the state quantity of each neuron), and it is necessary to reduce the complexity of the assimilation algorithm as much as possible while ensuring the assimilation effect, otherwise the computational cost required for assimilation is unbearable.

[0006] The core problem of this patent is to obtain the time series (calcium fluorescence signal) of calcium wave imaging of some neurons in zebrafish. Based on calcium wave imaging and a biological neuron model, a digital neuron system that generates a similar calcium wave sequence is implemented using numerical methods, where the unknown model parameters are approximated by a data assimilation algorithm. From the above discussion, there are the following difficulties in this problem: (1) The sampling frequency of the calcium wave signal is low (2 Hz) and it contains noise. (2) Only the calcium wave signals of some neurons are recorded. (3) It is difficult to observe the connection structure, types, etc. of neurons. (4) The computational complexity of simulating and assimilating a large-scale neuron system is high. Summary of the Invention

[0007] This invention is proposed to solve the above problems, and its purpose is to provide a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals.

[0008] This invention provides a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals, which has the following characteristics and includes the following steps: Step 1, estimate the probability distribution of neuron connections between different brain regions of zebrafish based on experimental data, and randomly generate a network connection structure according to the specified connection degree to obtain connection data. Step 2, calculate the neuron excitatory and inhibitory indicators based on the calcium wave imaging signals of zebrafish, and classify each neuron to obtain neuron type information. Step 3, based on the connection data and neuron type information, use the leaky integrate-and-fire model and the four-channel synaptic connection model to construct a zebrafish neural network model, then superimpose a dopamine regulation mechanism model and a calcium wave model on the model, and define the parameters in the system that need to be assimilated. Step 4, use the adjusted ensemble Kalman filter to perform data assimilation on the parameters that need to be assimilated until the correlation between the calcium wave data generated by the system during assimilation and the experimental data is high enough to obtain the assimilated system parameters. Step 5, use the assimilated system parameters for simulation testing, and observe the correlation between the calcium wave signals generated by the system and the experimental data. If the correlation is weak, repeat Step 4 until the correlation between the calcium wave data generated by the system during simulation and the experimental data is high enough to obtain the iterated assimilated parameters. Step 6, use the iterated assimilated parameters as the system parameters to complete the construction of the zebrafish neuron system.

[0009] In the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals provided by this invention, it can also have the following characteristics: Among them, in Step 1, define the probability distribution of the connections of each neuron in each brain region to the neurons in the same brain region and other brain regions, and generate an adjacency list according to the specified connection degree.

[0010] In the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals provided by the present invention, it may further have the following characteristics: wherein, in step 2, the type of neurons is estimated according to the sign of the correlation of calcium wave imaging signals between neurons.

[0011] In the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals provided by the present invention, it may further have the following characteristics: wherein, in step 3, the calcium wave model converts neuronal electrical signals into calcium signals.

[0012] In the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals provided by the present invention, it may further have the following characteristics: wherein, in step 3, for the parameters that do not participate in assimilation, they are estimated by combining experimental data and prior knowledge, and the parameters that do not participate in assimilation are unknown system parameters.

[0013] In the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals provided by the present invention, it may further have the following characteristics: wherein, in step 4, the process of data assimilation is as follows: the values of unknown parameters in the model are inferred from calcium wave data, and the initialization of the system and the settings of assimilation hyperparameters are adjusted according to the assimilation results until the correlation between the calcium wave data generated by the system during assimilation and the experimental data is high enough.

[0014] Functions and effects of the invention

[0015] According to the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals involved in the present invention, the specific steps are as follows: Step 1, based on experimental data, estimate the probability distribution of neuron connections between different brain regions of the zebrafish, and randomly generate a network connection structure according to the specified connection degree to obtain connection data; Step 2, calculate the neuron excitatory and inhibitory indexes based on the calcium wave imaging signals of the zebrafish, divide the type of each neuron to obtain neuron type information; Step 3, based on the connection data and neuron type information, construct a zebrafish neural network model using the leaky integrate-and-fire model and the four-channel synaptic connection model, then superimpose a dopamine regulation mechanism model and a calcium wave model on the model, and define the parameters to be assimilated in the system; Step 4, use the adjusted ensemble Kalman filter to perform data assimilation on the parameters to be assimilated until the correlation between the calcium wave data generated by the system during assimilation and the experimental data is high enough to obtain the assimilated system parameters; Step 5, use the assimilated system parameters for simulation testing, observe the correlation between the calcium wave signals generated by the system and the experimental data, if the correlation is weak, repeat step 4 until the correlation between the calcium wave data generated by the system during simulation and the experimental data is high enough to obtain the iterated assimilation parameters; Step 6, use the iterated assimilation parameters as the system parameters to complete the construction of the zebrafish neuron system.

[0016] Therefore, the present invention is mainly used for modeling and simulating the time series of calcium wave imaging of the model animal zebrafish, and combining with a neural network model for data assimilation to estimate system parameters, so as to construct a digital twin zebrafish nervous system with kinetic behavior close to that of real zebrafish. It can be used to efficiently simulate biological experiments, such as brain region ablation, drug stimulation, etc., and verify with existing experimental results. The quality of the assimilation result is measured by the correlation between the calcium wave sequence generated by system simulation and the experimental observation data.

[0017] In addition, the present invention can efficiently model, assimilate and then reconstruct the nervous system of zebrafish by using the experimental data of calcium signals of zebrafish, and ensure that the assimilation system is close enough to the real system. Specifically, the present invention can reduce the complexity of the ensemble Kalman filter algorithm, making it feasible for large-scale nervous systems; it can also efficiently simulate the nervous system of zebrafish with the help of a graph neural network library; it can also achieve good data assimilation effect of the nervous system of zebrafish based on limited observation data. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flowchart of a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] In order to make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the following embodiments will specifically describe a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals of the present invention in conjunction with the drawings.

[0020] In this embodiment, a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals is provided.

[0021] Figure 1 is a flowchart of a method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals in an embodiment of the present invention.

[0022] As Figure 1 shown, the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals involved in this embodiment includes the following steps:

[0023] Step S1, estimate the probability distribution of neuron connections between different brain regions of zebrafish based on experimental data, randomly generate a network connection structure according to the specified connection degree, and obtain connection data.

[0024] In this embodiment, the experimental data are the connection strength data of each brain region of zebrafish. To determine the connection structure of the neural network during simulation and assimilation, based on the experimental data, the probability distribution of the connections between neurons in different brain regions is estimated, and the network connection structure is randomly generated. That is, for each neuron in each brain region, the probability distribution of its connections to neurons in the same brain region and other brain regions can be defined. Thus, by specifying the connection degrees of each neuron, the network connection can be generated through a single random simulation.

[0025] Step S2: Calculate the neuron excitation and inhibition indexes based on the calcium wave imaging signals of zebrafish, and classify each neuron to obtain the neuron type information.

[0026] Since the type (excitatory neuron or inhibitory neuron) of each neuron is unknown, to determine the excitatory and inhibitory types of neurons, an index indicating that each neuron is an inhibitory neuron is given based on the calcium wave of each neuron and the calcium wave signals of its surrounding neurons, and the neurons are classified based on the experimentally measured excitatory and inhibitory ratios. That is, the type of neuron is estimated according to the sign of the correlation of calcium wave signals between neurons.

[0027] Define the following index: Calculate the proportion of the number of neighboring neurons of each neuron whose calcium signal correlation is less than a threshold value to the total number of its neighboring neurons. The neighboring neurons of a neuron are its k nearest neighbors in terms of spatial position (the position information of each neuron is required). Then, based on the excitatory and inhibitory neuron ratios of each brain region given by the experimental data, each neuron is classified.

[0028] Step S3: Construct a zebrafish neural network model based on the connection data and neuron type information. Subsequently, a dopamine regulation mechanism model and a calcium wave model are superimposed on the model, and the parameters to be assimilated in the system are defined.

[0029] In this embodiment, a relatively simple Leaky Integrated and Fire model is selected to model the neuron cell bodies of zebrafish, and a four-channel dopamine model is used to model the synaptic connections between neurons. For the calcium wave model, based on the research of calcium signal fluorescence imaging, a relatively simple linear autoregressive model is selected. To also consider the influence of unobserved neurons on the system, a dopamine regulation mechanism for the neuron firing threshold is constructed, and relevant parameters are assimilated. To ensure the feasibility of assimilation, the number of parameters to be assimilated is minimized as much as possible.

[0030] The specific process is as follows: Based on connection data and neuron type information, a leaky integrate-and-fire model and a four-channel synaptic connection model are used to construct a parametric zebrafish neural network model. Subsequently, a dopamine regulation mechanism model and a calcium wave model that converts neuronal electrical signals into calcium signals are superimposed on the system. The parameters to be assimilated are demarcated, and for unknown system parameters that do not participate in assimilation, they are estimated by combining experimental data and prior knowledge.

[0031] Step S4, use the adjusted ensemble Kalman filter to perform data assimilation on the system, that is, reverse-infer the values of unknown parameters in the model from the experimental calcium wave data. According to the assimilation results, adjust the settings such as the initialization of the system and the assimilation hyperparameters until the correlation between the calcium waves generated by the system during assimilation and the experimental data is high enough to obtain the assimilated system parameters.

[0032] In this embodiment, the traditional ensemble Kalman filter algorithm is improved. Combining the special structure of the neural network dynamic system, a scheme of dividing the system into multiple subsystems for assimilation separately is proposed, reducing the computational complexity from cubic with respect to the number of neurons to linear with respect to the number of neurons, and parallelizing with the help of the message passing mechanism provided by the graph neural network computing library, so that large-scale and simulated assimilation numerical experiments can be efficiently carried out.

[0033] Step S5, use the assimilated system parameters for simulation tests, and observe the correlation between the calcium wave signals generated by the system and the experimental data. If the correlation is weak, repeat Step S4 to reconfigure the assimilation and conduct a new assimilation experiment until the simulated system can generate a calcium wave sequence with a high enough correlation with the experimental data to obtain the iterated assimilation parameters.

[0034] Step S6, take the finally iterated assimilation parameters as the system parameters to complete the construction of the zebrafish neuron system.

[0035] Functions and effects of the embodiment

[0036] According to the method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals involved in this embodiment, the specific steps are as follows: Step 1, estimate the probability distribution of neuron connections between different brain regions of the zebrafish based on experimental data, and randomly generate a network connection structure according to the specified connection degree to obtain connection data; Step 2, calculate the neuron excitatory and inhibitory indexes based on the calcium wave imaging signals of the zebrafish, and classify each neuron to obtain neuron type information; Step 3, based on the connection data and neuron type information, construct a zebrafish neural network model using the leaky integrate-and-fire model and the four-channel synaptic connection model, then superimpose a dopamine regulation mechanism model and a calcium wave model on the model, and define the parameters in the system that need to be assimilated; Step 4, use the adjusted ensemble Kalman filter to perform data assimilation on the parameters that need to be assimilated until the correlation between the calcium wave data generated by the system during assimilation and the experimental data is high enough to obtain the assimilated system parameters; Step 5, use the assimilated system parameters for simulation testing, observe the correlation between the calcium wave signals generated by the system and the experimental data. If the correlation is weak, repeat Step 4 until the correlation between the calcium wave data generated by the system during simulation and the experimental data is high enough to obtain the iteratively assimilated parameters; Step 6, use the iteratively assimilated parameters as the system parameters to complete the construction of the zebrafish neuron system.

[0037] Therefore, the above embodiment is mainly used to model and simulate the time series of calcium wave imaging of the model animal zebrafish and perform data assimilation in combination with a neural network model to estimate system parameters, so as to construct a digital twin zebrafish nervous system with dynamic behavior close to that of real zebrafish. It can be used to efficiently simulate biological experiments such as brain region ablation and drug stimulation, and verify with existing experimental results. The quality of the assimilation result is measured by the correlation between the calcium wave sequence generated by system simulation and the experimental observation data.

[0038] In order to efficiently model, assimilate and then reconstruct the nervous system of zebrafish using the experimental data of zebrafish calcium signals, and ensure that the assimilation system is close enough to the real system. Specifically, this embodiment can reduce the complexity of the ensemble Kalman filter algorithm, making it feasible for large-scale nervous systems; it can also efficiently implement the simulation of the zebrafish nervous system with the help of a graph neural network library; and it can also achieve good data assimilation effects for the zebrafish nervous system based on limited observation data.

[0039] The above embodiment is a preferred case of the present invention and does not limit the protection scope of the present invention.

Claims

1. A method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals, characterized in that Including the following steps: Step 1: Estimate the probability distribution of neuron connections between different brain regions of zebrafish based on experimental data, and randomly generate a network connection structure according to the specified connection degree to obtain connection data; Step 2: Calculate the neuron excitatory and inhibitory indicators based on the calcium wave imaging signals of zebrafish, and classify each neuron to obtain neuron type information; Step 3: Based on the connection data and the neuron type information, construct a zebrafish neural network model using the leaky integrate-and-fire model and the four-channel synaptic connection model. Subsequently, superimpose a dopamine regulation mechanism model and a calcium wave model on the model, and define the parameters in the system that need to be assimilated; Step 4: Use the adjusted ensemble Kalman filter to perform data assimilation on the parameters that need to be assimilated until the correlation between the calcium wave data generated by the system during assimilation and the experimental data is high enough to obtain the assimilated system parameters; Step 5: Use the assimilated system parameters for simulation testing, and observe the correlation between the calcium wave signals generated by the system and the experimental data. If the correlation is weak, repeat Step 4 until the correlation between the calcium wave data generated by the system during simulation and the experimental data is high enough to obtain the iterated assimilated parameters; Step 6: Use the iterated assimilated parameters as system parameters to complete the construction of the zebrafish neuron system.

2. The method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals according to claim 1, wherein: Among them, In Step 1, define the probability distribution of the connections of each neuron in each of the brain regions to the neurons in the same brain region and other brain regions, and generate an adjacency list according to the specified connection degree.

3. The method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals according to claim 1, wherein: Among them, In Step 2, estimate the type of the neuron according to the sign of the correlation of the calcium wave imaging signals between the neurons.

4. The method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals according to claim 1, wherein: Among them, In Step 3, the calcium wave model converts neuron electrical signals into calcium signals.

5. The method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals according to claim 1, wherein: Among them, In Step 3, for the parameters that do not participate in assimilation, estimate them by combining experimental data and prior knowledge, and the parameters that do not participate in assimilation are unknown system parameters.

6. The method for constructing a digital twin zebrafish nervous system based on calcium wave imaging signals according to claim 1, wherein: Among them, In Step 4, the process of data assimilation is as follows: deduce the values of the unknown parameters in the model from the calcium wave data, and adjust the initialization of the system and the settings of the assimilation hyperparameters according to the assimilation results until the correlation between the calcium wave data generated by the system during assimilation and the experimental data is high enough.

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