CN113643749A - Method and system for constructing model of grid cells - Google Patents
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Abstract
The invention discloses a method and a system for constructing a model of grid cells, wherein the method comprises the following steps: s1, modeling the grid cell group by adopting a two-dimensional plane continuous attractor model; s2, constructing a neural plate consisting of grid cells in planar distribution; s3, encoding a path integration result in a specific direction by using the fringe discharge generated in the fringe cells; s4, discharging and projecting plasma cells of a plurality of stripe cell groups with the same spacing in different directions onto the same grid cell neural plate; and S5, generating a superposition discharge response by using the grid cells to form grid discharge. Has the advantages that: the invention provides that the striped cell discharge is used as the forward signal input of the grid cells, a plurality of flowing striped waves jointly drive the grid cells to encode the space, and a flowing two-dimensional discharge grid is formed, so that the information transmission and processing mode accords with the physiological basis.
Description
Technical Field
The invention relates to the technical field of neurobiology model construction, in particular to a method and a system for constructing a model of grid cells.
Background
Moser couples found lattice cells in the second layer of the olfactory cortex in rat hippocampus, but unlike the site cells and head-oriented cells, lattice cells were more dispersed and discharges were weaker. As shown in fig. 4, the lattice cells in different regions along the dorsoventral axis in the entorhinal cortex have different lattice period scales, the discharge regularity of the lattice cell groups of each scale is basically the same, and the discharge fields form a stable hexagonal structure and form an included angle of 120 degrees with each other.
Hafting et al designed experiments with transform chamber sizes to further verify the presence of grid cells. When rats explore an unknown environment, the network of lattice cells changes and then remains stable. The network of grid cells remains substantially unchanged even if the environment changes greatly during animal movement. Each grid cell has more than one discharge field, and when the rat moves to some specific position in the space, the grid cells are discharged. The discharge activity of the grid cells is not dependent on external clues, the rat is placed in a dark environment, and the activity mode of the grid cells cannot be changed as long as a new environment is not changed. And the grid field of the grid cells can always cover all areas of the spatial environment, biologists guess that grid cells may have a path integration effect on the space.
Previous research models only used head-oriented and location cells to construct cognitive maps of arbitrary dimensional spatial relationships, and this discrete expression of individual head-oriented and location cellular activities was not sufficient to support navigational behavior from one location to another. The grid cells provide main information input for the position cells, and are path integrators inside the brain, and the periodic discharge field of the grid cells can cover the whole spatial environment along with the exploration of animals in the environment, so that the grid cells provide spatial measurement for the formation of a cognitive map. Therefore, the invention provides a method and a system for constructing a model of grid cells.
Disclosure of Invention
The invention provides a method and a system for constructing a grid cell model, aiming at the problems in the related art, so as to overcome the technical problems in the prior related art.
Therefore, the invention adopts the following specific technical scheme:
according to an aspect of the present invention, there is provided a method of constructing a model of lattice cells, the method comprising the steps of:
s1, modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;
s2, constructing a neural plate consisting of grid cells in planar distribution;
s3, encoding a path integration result in a specific direction by using the fringe discharge generated in the fringe cells;
s4, discharging and projecting plasma cells of a plurality of stripe cell groups with the same spacing in different directions onto the same grid cell neural plate;
and S5, generating a superposition discharge response by using the grid cells to form grid discharge.
Further, the attractors in the attractor model in S1 represent grid cells, and the activity states of the grid cells are associated with the forward input of the upstream striped cells.
Further, the activation input of each grid cell in S2 is obtained from the striped cells in each direction on the corresponding phase.
Further, the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents a distance between adjacent discharge fields, the grid orientation represents an inclination angle of a connecting line between the nodes of the discharge fields relative to an external reference point, and the grid phase represents a displacement relative to the external reference point.
Further, the discharge kinetics model of the streak cells is as follows:
where τ represents the time constant of the neuron, and the neuron transfer function f is a simple nonlinear rectification function when x is>When 0, f (x) is x, when x is<When 0, f (x) is 0, the discharge state of the neuron i at the current position is si，WijIs the weight, Σ, of the connection from neuron j to neuron i in the strip neural platejWijsjIs an inhibitory recursive input, B, projected onto neuron iiIs a forward excitatory input from the upstream head towards the cell;
the connection weight matrix of the stripe cells is as follows:
wherein,
denotes the edge thetajUnit vector of direction.
According to another aspect of the present invention, a grid cell model construction system is provided, which includes a grid cell group modeling module, a neural plate construction module, a path integration result coding module, a discharge projection module, and a grid discharge module;
the grid cell group modeling module is used for modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;
the neural plate construction module is used for constructing a neural plate consisting of grid cells distributed in a plane;
the path integration result coding module is used for coding a path integration result in a specific direction by using fringe discharge generated in fringe cells;
the discharge projection module is used for projecting plasma cells of a plurality of stripe cell families with different directions and the same interval to the same grid cell neural plate in a discharge manner;
the grid discharge module is used for generating superposition discharge response by utilizing grid cells to form grid discharge.
Further, attractors in the attractor model represent grid cells, and the activity state of the grid cells is related to the forward input of the upstream stripe cells.
Further, the activation input for each of the grid cells is derived from striped cells in respective directions on the corresponding phase.
Further, the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents a distance between adjacent discharge fields, the grid orientation represents an inclination angle of a connecting line between the nodes of the discharge fields relative to an external reference point, and the grid phase represents a displacement relative to the external reference point.
The invention has the beneficial effects that: the invention provides a method for coding a space by using stripe cell discharge as a forward signal input of grid cells and jointly driving the grid cells to encode the space by a plurality of flowing stripe waves to form a flowing two-dimensional discharge grid, so that an information transmission and processing mode accords with physiological basis; in addition, the invention drives the stripe cells to discharge modal flow when the rat moves, so that the grid cells also generate a flowing discharge grid, thereby realizing the integration of the grid cells to the spatial path information.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments 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 it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for constructing a model of a lattice cell according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of grid characteristic parameters in a method for constructing a model of grid cells according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a principle of encoding a grid cell model in a method for constructing a model of grid cells according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a striped cell neural plate model in a method for constructing a grid cell model according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating a Mexican hat weight profile in a method for constructing a model of a lattice cell according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a stripe cell weight shift contour in a method for constructing a model of grid cells according to an embodiment of the present invention.
Detailed Description
For further explanation of the various embodiments, the drawings which form a part of the disclosure and which are incorporated in and constitute a part of this specification, illustrate embodiments and, together with the description, serve to explain the principles of operation of the embodiments, and to enable others of ordinary skill in the art to understand the various embodiments and advantages of the invention, and, by reference to these figures, reference is made to the accompanying drawings, which are not to scale and wherein like reference numerals generally refer to like elements.
According to the embodiment of the invention, a method and a system for constructing a model of grid cells are provided.
Referring now to the drawings and the detailed description, a method for constructing a model of a lattice cell is provided according to an embodiment of the present invention, as shown in fig. 1-6, and includes the following steps:
s1, modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;
wherein each attractor in the attractor model represents a lattice cell, and the activity state of the lattice cell is related to the forward input of the upstream striped cell.
S2, constructing a neural plate consisting of grid cells in planar distribution;
in S2, each grid cell obtains an activation input from the stripe cells in each direction on the corresponding phase, that is, the stripe discharge information is superimposed.
S3, encoding a path integration result (namely, relative displacement) in a specific direction by using the fringe discharge generated in the fringe cells;
according to the attractor model theory, a strip-shaped neural plate as shown in fig. 4 is constructed in this embodiment, and there is synapse connection between neurons in the length direction and no connection in the width direction. Each neural plate may respond to electrical discharges in a particular direction depending on the preferential direction of its upstream head towards the cell. The neurons generate periodic discharges driven by the speed information encoded towards the cells by the upstream head, so that flowing fringe waves are generated on the neural plate, and the position of the rat can be encoded according to the phase change of the fringe waves. The exploration environment of the robot cannot be measured, and the size of the neuron panel is limited, which inevitably involves the boundary problem of the attractor network. In order to solve this problem, neurons on both sides in the longitudinal direction of the strip-shaped neural plate are connected to form a circular continuous attractor model.
Because the neurons in the width direction of the strip-shaped neural plate are not connected, the discharge responses are independent, and only the phase in the length direction is considered during model calculation. To form the striated firing characteristics, synaptic connection weights between lengthwise neurons are set to be mutually inhibitory, and the velocity modulation signal generated by the head towards the cell is used as the forward input to the striated cell. The following streak cell discharge kinetics model based on discharge rate can be constructed as follows:
where τ represents the time constant of the neuron, and the neuron transfer function f is a simple nonlinear rectification function when x is>When 0, f (x) is x, when x is<When 0, f (x) is 0, the discharge state of the neuron i at the current position is si，WijIs the weight, Σ, of the connection from neuron j to neuron i in the strip neural platejWijsjIs an inhibitory recursive input, B, projected onto neuron iiIs a forward excitatory input from the upstream head towards the cell;
in order to realize the driving of stripes by the forward excitation input from the head to the cells, the neurons i and i +1 of the left and right adjacent phases are set to correspond to two types of upstream head-oriented cells with opposite priority directions, and the inhibitory weight matrix of the neuron to the peripheral neuron is set to be deviated towards the priority direction. When there is only inhibitory input between neurons, the neural plate spontaneously develops a steady-state striated discharge. When there is a forward excitation input, only the half of neurons with the same priority direction obtain excitation input, and the input of the other half of neurons with the opposite priority directions is zero, so that the original steady state is broken, the weight matrix of the inhibitory input of peripheral neurons to all the neurons can shift towards the speed direction, and further strip ripples are driven to generate coupled motion with the speed.
The connection weight matrix of the stripe cells is as follows:
wherein,
denotes the edge thetajThe unit vectors of the directions, as shown in FIG. 5, form a Mexican hat-shaped distribution with a high middle and two low sides. Setting the projected weight matrix of each neuron will shift k neuron positions along the preferential direction, and since the adjacent neurons on the neural plate have opposite preferential directions, as shown in fig. 6, the central position of the neural cell weight matrix is x-k, x + k. We set γ to 1.05 × β, β to 3/λ2And λ is the period of striations formed on the neural plate. When a is 1, all linkages are inhibitory, and local peripheral inhibitory linkages produce a striped cellular response through interaction.
The forward inputs on neuron i are:
wherein,
representing a unit vector along the preferential direction in which neuron i is located,
is a unit vector in the direction of the current speed of the rat. If the coefficient k or a is 0, a static streak is generated. If both k and a are non-0, the velocity of the rat
Coupled with the dynamics of the striated neural plate, drives the stripe ripple that forms the flow. The product of k and a determines the strength of the velocity input to the fringe stream drive. The stripe ripple can maintain a stable stripe pattern only when the output weight offset k is small. On the basis of k being fixed, the gain of the stripe cell network to the speed response is determined by a. If it is not
Much less than 1, the input speed drive does not disrupt the stripe pattern that has been formed.
S4, discharging and projecting plasma cells of a plurality of stripe cell groups with the same spacing in different directions onto the same grid cell neural plate;
and S5, generating a superposition discharge response by using the grid cells to form grid discharge.
As shown in fig. 2, the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing (λ), grid orientation (θ) and grid phase (Δ x, Δ y), wherein the grid spacing represents the distance between adjacent discharge fields, the grid orientation represents the inclination angle of the connecting line between the discharge field nodes with respect to the external reference point, and the grid phase represents the displacement with respect to the external reference point.
According to another embodiment of the present invention, a grid cell model construction system is provided, which includes a grid cell population modeling module, a neural plate construction module, a path integration result coding module, a discharge projection module, and a grid discharge module;
the grid cell group modeling module is used for modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;
the neural plate construction module is used for constructing a neural plate consisting of grid cells distributed in a plane;
the path integration result coding module is used for coding a path integration result in a specific direction by using fringe discharge generated in fringe cells;
the discharge projection module is used for projecting plasma cells of a plurality of stripe cell families with different directions and the same interval to the same grid cell neural plate in a discharge manner;
the grid discharge module is used for generating superposition discharge response by utilizing grid cells to form grid discharge.
Wherein each attractor in the attractor model represents a lattice cell, and the activity state of the lattice cell is related to the forward input of the upstream striped cell; the activation input of each grid cell is obtained from the stripe cells in all directions on the corresponding phase; the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents the distance between adjacent discharge fields, the grid orientation represents the inclination angle of a connecting line between the nodes of the discharge fields relative to an external reference point, and the grid phase represents the displacement relative to the external reference point.
In summary, with the above technical solution of the present invention, the present invention provides that the striped cell discharge is input as a forward signal of the grid cell, and multiple flowing striped waves jointly drive the grid cell to encode the space, so as to form a flowing two-dimensional discharge grid, so that the information transmission and processing manner conforms to the physiological basis; in addition, the invention drives the stripe cells to discharge modal flow when the rat moves, so that the grid cells also generate a flowing discharge grid, thereby realizing the integration of the grid cells to the spatial path information.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (9)
1. A method for constructing a model of a lattice cell, the method comprising the steps of:
s1, modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;
s2, constructing a neural plate consisting of grid cells in planar distribution;
s3, encoding a path integration result in a specific direction by using the fringe discharge generated in the fringe cells;
s4, discharging and projecting plasma cells of a plurality of stripe cell groups with the same spacing in different directions onto the same grid cell neural plate;
and S5, generating a superposition discharge response by using the grid cells to form grid discharge.
2. The method of claim 1, wherein the attractors in the attractor model in S1 represent grid cells, and the activity status of the grid cells is associated with the forward input of the upstream striped cells.
3. The method of claim 1, wherein the activation input of each grid cell in S2 is obtained from striped cells in each direction on the corresponding phase.
4. The method of claim 1, wherein the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents a distance between adjacent discharge fields, the grid orientation represents a tilt angle of a connecting line between the nodes of the discharge fields relative to an external reference point, and the grid phase represents a displacement relative to the external reference point.
5. The method of claim 1, wherein the model of the grid cells is obtained by performing a discharge dynamics modeling of the striped cells as follows:
where τ represents the time constant of the neuron, and the neuron transfer function f is a simple nonlinear rectification function when x is>When 0, f (x) is x, when x is<When 0, f (x) is 0, the discharge state of the neuron i at the current position is si，WijIs the weight, Σ, of the connection from neuron j to neuron i in the strip neural platejWijsjIs an inhibitory recursive input, B, projected onto neuron iiIs a forward excitatory input from the upstream head towards the cell;
the connection weight matrix of the stripe cells is as follows:
wherein,
denotes the edge thetajUnit vector of direction.
6. A grid cell model construction system for implementing the steps of the grid cell model construction method according to any one of claims 1 to 5, wherein the system comprises a grid cell group modeling module, a neural plate construction module, a path integration result coding module, a discharge projection module and a grid discharge module;
the grid cell group modeling module is used for modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;
the neural plate construction module is used for constructing a neural plate consisting of grid cells distributed in a plane;
the path integration result coding module is used for coding a path integration result in a specific direction by using fringe discharge generated in fringe cells;
the discharge projection module is used for projecting plasma cells of a plurality of stripe cell families with different directions and the same interval to the same grid cell neural plate in a discharge manner;
the grid discharge module is used for generating superposition discharge response by utilizing grid cells to form grid discharge.
7. The system of claim 6, wherein the attractors in the attractor model represent grid cells, and the activity state of the grid cells is associated with the forward input of the upstream striped cells.
8. The system of claim 6, wherein the activation input for each of the grid cells is derived from striped cells in each direction on the corresponding phase.
9. The system of claim 6, wherein the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents a distance between adjacent discharge fields, the grid orientation represents a tilt angle of a line between nodes of the discharge fields relative to an external reference point, and the grid phase represents a displacement relative to the external reference point.
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