Oscillatory Tracking of Continuous Attractor Neural Networks Account for Phase Precession and Procession of Hippocampal Place Cells
Abstract
Hippocampal place cells of freely moving rodents display an intriguing temporalorganization in their responses known as ‘theta phase precession’, in which individual neurons fire at progressively earlier phases in successive theta cycles as theanimal traverses the place fields.
Recent experimental studies found that in additionto phase precession, many place cells also exhibit accompanied phase procession,but the underlying neural mechanism remains unclear.
Here, we propose a neuralcircuit model to elucidate the generation of both kinds of phase shift in place cells’firing.
Specifically, we consider a continuous attractor neural network (CANN)with feedback inhibition, which is inspired by the reciprocal interaction betweenthe hippocampus and the medial septum.
The feedback inhibition induces intrinsicmobility of the CANN which competes with the extrinsic mobility arising fromthe external drive.
Their interplay generates an oscillatory tracking state, that is,the network bump state (resembling the decoded virtual position of the animal)sweeps back and forth around the external moving input (resembling the physicalposition of the animal).
We show that this oscillatory tracking naturally explainsthe forward and backward sweeps of the decoded position during the animal’slocomotion.
At the single neuron level, the forward and backward sweeps accountfor, respectively, theta phase precession and procession.
Furthermore, by tuning thefeedback inhibition strength, we also explain the emergence of bimodal cells andunimodal cells, with the former having co-existed phase precession and procession,and the latter having only significant phase precession.
We hope that this studyfacilitates our understanding of hippocampal temporal coding and lays foundationfor unveiling their computational functions.
Introduction
The mammalian hippocampus is responsible for spatial navigation [1, 2] and episodic memory [3, 4,5, 6].
Rodent studies have revealed two prominent firing features of hippocampal place cells duringanimals’ locomotion.
First, each place cell has localized spatial coding which fires in restrictedregions of a given environment (place fields)
Second, the firing of a place cell displays detailedtemporal organization known as ‘theta phase precession’, whereby neuronal spikes are elicited atsuccessively earlier phases of the theta cycles of the local field potential (LFP) as the animal travelsthrough the place field (Fig.
1A) [9, 10].
This phase precession of individual neurons results in that theactivities of consecutively activated place cells along the animal’s moving trajectory are compressedinto a firing sequence within a theta cycle, named forward theta sequence (Fig.
1A)
It has been hypothesized that such theta sequences compress sequential responses of neurons at thebehavioral timescale (seconds) into the theta-cycle timescale (tens of milliseconds) in a temporally
A
B The animal’s trajectory
Place fields a b c d e
Forward Theta sequences a b c d e
Phase precession
Time {+
+}
P l a c e c e ll ne t w o r k  t he t a 1 24 5 neu r on i d x phase precession phase precession {+theta cycles 0 1 2 
+}
Recurrent input
Feedbackinhibition
External input -V(x,t) ,
I (x,t) ext r(x,t)
C
Output } }
HPC
MS = =
[Figure] [Figure]
[Figure]
[Figure]
D ordered way, which is short enough to enable spike-time-dependent plasticity (STDP) betweenneurons [15, 16].
Thus, theta phase precession may serve as a neural substrate for the formation ofspatial and episodic memories [17].
Recently, experimental studies found that in addition to phase precession, many place cells inthe hippocampus of freely moving rodents also exhibit phase procession, i.e., a place cell fire atprogressively later phases in successive theta cycles as the animal traverses the place field (Fig.1B)
Analogy to the formation of forward theta sequences, phase procession of place cellsfiring consecutively along the animal’s moving trajectory results in reverse theta sequences.
Fromthe view of information processing, phase precession and procession correspond respectively, to theprospective and retrospective evaluations of animals’ ongoing behaviors, which further supports theforward and reverse replays during memory consolidation [23, 24, 25, 26].
Instead of existing alonein a theta cycle, a recent study showed that the reverse theta sequence co-exists with the forwardtheta sequence in individual theta cycles [27] (Fig. 1B).
As it has far-reaching implications to brainfunctions, a large volume of modelling studies has been devoted to understand the generation oftheta phase precession of place cells.
These models can be roughly divided into two categories, withone focusing on the mechanism of single cell oscillation [9, 28, 29, 30, 31] and the other on themechanism of recurrent interactions between neurons [32, 33, 34] (see more discussions in Sec. 5).
However, these models have not accommodated the newly found phase procession which co-existswith phase precession in theta cycles, and hence need to be re-evaluated.
In the current study, we propose a neural circuit model to elucidate the underlying mechanism ofthe co-occurrence of phase precession and procession in individual theta cycles, as well as manyother recent experimental findings.
Specifically, we consider a continuous attractor neural network(CANN) with feedback inhibition (Fig. 1C).
The CANN is a conceptualized circuit model for thenetwork of place cells [35, 36, 37, 38], and the feedback inhibition models the interplay between thehippocampus and the medial septum with reciprocally connected GABAergic neurons [39, 40, 41, 42](Fig.
1D).
Without feedback inhibition, the CANN holds a localized bump-shaped activity state(resembling the decoded virtual position of the animal), which can smoothly track the movement ofthe external input (resembling the physical position of the animal).
When a strong enough feedbackinhibition is added, it destabilizes the neuronal firing and induces intrinsic mobility of the bumpactivity.
This intrinsic mobility competes with the extrinsic mobility (arising from the external drive)and causes an oscillatory tracking state, i.e., the network bump sweeps back and forth around theexternal moving input.
Intriguingly, we find that this oscillatory tracking naturally gives rise to thephase shift of place cell firing during animals’ locomotion.
At the neuron ensemble level, the forwardand backward bump sweeps account for, respectively, the forward and reverse theta sequences of theplace cell ensemble.
At the single neuron level, individual neurons in the CANN exhibit both phaseprecession and procession as the external input travels through their firing fields, with precession and procession occurring in the forward and backward bump sweeps, respectively.
Moreover, we findthat the feedback inhibition strength is the key for generating different phase shift patterns in placecell firing.
With a weak feedback inhibition, all the neurons in the CANN are bimodal cells, whichpossess co-existed phase precession and procession in their firings.
With a strong feedback inhibition,all the neurons in the CANN are unimodal cells, which possess only significant phase precession intheir firings.
We also theoretically elucidate the underlying network dynamics for producing thesefiring behaviours.
We hope that this study helps us to unveil the underlying mechanism of phaseshifts of place cells, and sheds light on our understanding of temporal coding of hippocampal neuronsand the related functions in spatial navigation and episodic memory.
The Computational Model2.1 A CANN with feedback inhibition
For simplicity, we study a one-dimensional (1D) CANN (modeling animals’ free moving on lineartracks), and results can be naturally generalized to the 2D case.
The 1D CANN is a conceptualizedcircuit model of the place cell ensemble, which consists of neurons arranged conceptually on a1-dimensional neuronal track according to their relative firing locations (Fig. 1C).
It is noteworthy thatthe relative location of two neurons on the neuronal track is irrelevant with their relative anatomicallocation in the hippocampus, i.e., neurons situated in the CANN can be viewed as place cells beingre-arranged according to their place fields during animals’ locomotion on the linear track.
Denote
U ( x, t ) as the synaptic input received by the neuron at location x , with x ∈ ( −∞ , ∞ ) , and r ( x, t )the corresponding firing rate.
The dynamics of the CANN is written as,
[Equation]
where τ is the neuron time constant, and ρ represents the neuron density.
The recurrent connectionsare translation-invariant, which is given by J ( x, x ′ )
=
J 0 / (2 πa ) exp (cid:2) − ( x − x ′ ) 2 / (2 a 2 ) (cid:3) , with
J 0 the maximum connection strength and a the range of neuronal interactions.
I ext ( x, t ) is theexternal input to the CANN, which resembles the physical location of the animal moving on thelinear track.
The nonlinear relationship between the firing rate r ( x, t ) and the synaptic input U ( x, t )is implemented by the divisive normalization, whose strength is controlled by k in the denominatorof Eq.2, and g is a gain factor.
The divisive normalization implicitly models the contribution ofinhibitory neurons to the pyramidal neurons, which could be implemented by shunting inhibitionin the real neural system [43].
It has been shown that with k < ρJ 20 / (8 √ 2 πa ) , the CANN holdsa continuous family of Gaussian-shaped stationary states (bump states), and these bumps form amanifold on which the network is neutrally stable [44, 45] (how the network bump state tracks theexternal input will be discussed in Sec. 2.2).
V ( x, t ) in Eq.
1 represents the feedback inhibition received by each neuron at location x , whosedynamics is written as,
[Equation]
where τ v is the time constant of V ( x, t ) , and τ v ≫ τ holds, implying that the feedback inhibition isa much slower process compared to the neuronal response.
The parameter m controls the strengthof feedback inhibition, i.e., the larger the m , the stronger the inhibition.
It is noteworthy that thefeedback inhibition described in Eq.
3 does not simply mean that neurons in the medial septumreceive direct excitatory input from neurons in the CANN and in turn inhibit them accordingly, butinstead, represents an overall effect of the interplay between the hippocampus and the medial septum.
This interplay may be implemented by the long-range reciprocal projections via GABAergic neuronsin the hippocampo-septo-hippocampo loop [46, 40, 47, 48] (see more discussion in Sec. 5).
2.2 Tracking behaviors of the CANN with feedback inhibition
In this section, we show how the network bump (internal representation) tracks the external input(external physical location).
Without loss of generality, we consider that the external input to the
CANN has the following Gaussian form:
[Equation]
where v ext represents the moving speed of the external bump input (resembling the moving speedof the animal on the linear track), and α controls the strength of the external input.
It is known thatwithout the external input drive, i.e., α = 0 , the network bump can move spontaneously due to thedestabilization of neural firing by the feedback inhibition (Fig. 2A).
Specifically, when m > τ/τ v ,the bump moves with an speed v int =
(2 a/τ v ) (cid:113) mτ v /τ − (cid:112) mτ
v /τ [49] (see Fig.
2B and SI.2 forthe mathematical derivation).
We term this spontaneously moving as the intrinsic mobility hereafter,which is independent of the external drive.
When both the external input (from sensory drive) and the feedback inhibition (from the interactionwith the medial septum) are applied to the CANN, the bump mobility is determined by these twofactors in a competitive way, that is, the external input tends to drive the bump to move at thespeed v ext , and the feedback inhibition tends to drive the bump to move at the intrinsic speed v int .
Depending on the relative strengths of these two factors (controlled by α and m in Eq. 4 and Eq.
3,respectively), the network exhibits three different tracking behaviors as summarized in Fig.
2C.
Specifically, we can study the tracking behaviors by fixing one parameter while varying the other.
While fixing the external input strength α and varying the feedback inhibition strength m , we have
• Travelling wave : when the feedback inhibition is relatively strong (large m ), the network holds
the travelling wave state (Fig. 2D) , in term of that the bump moves spontaneously at the
speed of v int , independent of the external input.
This is understandable: although the external input tends to attract the network bump the feedback inhibition has a stronger force to push it away, which causes the bump to move with its
intrinsic speed.
[Figure]
• Smooth tracking : when the feedback inhibition is relatively weak (small m ), the network holds [Figure] the state of smooth tracking (Fig. 2E), in term of that the bump is completely attracted by the [Figure]
external input and moves at the speed v ext .
This is because the feedback inhibition is not strong [Figure] enough to push the network bump away. [Figure]
which always lags
• Oscillatory tracking : when the feedback inhibition is moderate, the network holds the state ofoscillatory tracking (Fig.
2F), in term of that the overall motion of the bump follows the external moving input, while its position oscillates around the instant position of the external input.
This
oscillatory tracking originates from the competition between the intrinsic mobility caused by the feedback inhibition and the drive of the external moving input, which we explain in details below
2.3 The oscillatory tracking state
In this section, we present the analytical solution of the network model in the parameter regime ofoscillatory tracking (see SI.3 for mathematical details).
Due to the Gaussian-like neuronal connectionsand global inhibition (Eq. 2), we find that the network states in Eq.
1- 3 can be approximated as
Gaussian forms, which are expressed as:
[Equation]
Here A u ( t ) , A r ( t ) and A v ( t ) denote the bump heights at time t (note that U ( x, t ) , r ( x, t ) and V ( x, t )all have bump-shaped profiles).
z ( t ) denotes the position of bump centers of U ( x, t ) and r ( x, t ) ,which are always phase-locked on the neuronal track.
d ( t ) is the displacement of the bump centersbetween U ( x, t ) and V ( x, t ) , due to the delayed feedback inhibition with respect to the neuronalresponse in the CANN (see Fig.
2A).
For studying the bump oscillation, we focus on the dynamics ofz ( t ) , as the bump-shaped profiles remain unchanged across time.
From the simulation (Fig. 2F), weassume z ( t ) can be expressed as:
[Equation]
Here, s ( t ) denotes the displacement between the centers of the network bump and the external bump attime t (Fig.
3A), which oscillates as a sine wave.
c 0 and ω are positive values, denoting, respectively,the amplitude and the frequency of oscillation.
d 0 > 0 is a constant representing the positive offsetof bump oscillation with respect to the trajectory of the external input, which is observed in theexperiment (see Fig.1 in SI.4).
To obtain the parameter values c 0 , ω and d 0 in Eq.
8, we can simplifythe analysis by transforming the network dynamics into a low-dimensional space [45, 50].
This canbe done by projecting the network dynamics (after substituting Eq.
5-7 into Eq.
1- 3) onto the motionmodes that dominate the dynamics of the CANN, i.e., the bump position on the attractor manifold [Figure] shown in Fig. 2C and the bump height (see SI.2 & 3 for the detailed derivation).
The oscillation frequency is calculatedto be (for other parameter values, see SI.1),
[Equation]
Notably, the oscillation frequency ω scales sublinearly with both the strength of the external input αand the feedback inhibition m (see the phase diagram in Fig.
3B).
Increasing the strength of externalinput or the feedback inhibition enables the network bump to oscillate more frequently, and thesimulation results agrees well with the theoretical analysis (Fig.
3C).
Additionally, the expression in
Eq. 9 depends on other parameters such as the neuronal interaction range a
and the global inhibitionstrength k , which allows us to tune the oscillation frequency into the range of theta band.
We showbelow that this oscillatory tracking behavior naturally accounts for the forward and reverse thetasequences discovered in the hippocampus.
Oscillatory tracking accounts for the co-occurrence of phase precession andprocession
Early rodents studies widely found the canonical forward theta sequences in animals’ locomotion [10,13, 14, 51], where the decoded position from the place cell population activity sweeps in positionstarting slightly behind the animal and ending ahead of it in individual theta cycles.
A recent studyre-examined this finding with a large cell population on a fine time scale, and found that the decodedvirtual position rarely progresses exclusively in a single direction, but instead, progresses in bothdirections, with one traveling ahead of the animal and the other moving backward in the reversedirection of the movement (Fig.
4A upper panel)
We show that the co-occurrence of forwardand backward sweeps of the decoded position in individual theta cycles is naturally given by theoscillatory tracking behavior in our model.
In our model, the external bump input represents thephysical location of the rat on the linear track, and the network bump represents the decoded locationfrom the place cell population activity.
In each theta cycle, the network bump sweeps around theexternal bump in the forward and backward direction alternatively, which is analogy to the forwardand reverse theta sequences found in the experiment (Fig.
4A lower panel).
Additionally, our modelpredicts a positive offset d 0 > 0 in oscillatory tracking, as indicated by the experiment [27] (seedetailed description in SI.4).
Below we show that the forward and backward sweeps during the oscillatory tracking in the CANNaccount for, respectively, the phase precession and procession of individual place cells.
Without lossof generality, we study the firing phases of the neuron located at x = 0 (referred to as the probeneuron).
Replacing z ( t ) in Eq.
6 with the expression in Eq.
8, we obtain the firing response of the
[Figure]
neuron as the animal moving through the place field (adapted from the experimental data [10]). C. The enlarged view of phase precession and procession in the box in B (upper two panels), and the phases of the firing peak of the probe neuron in individual theta cycles (third panel). For parameter settings of producing these figures, see SI.1 and the uploaded code.
probe neuron at time t as [Equation] [Equation] where h ( t ) = v ext t + c 0 sin ωt + d 0 represents the displacement between the network bump centerand the location of the probe neuron (Fig.
4B second panel).
In the following discussion, we willrefer to the time as the external bump reaches the location of the probe neuron as t = 0 , with t < 0representing the external bump moving on the left-side of the probe neuron and t > 0 representingthe bump moving on the right-side of the probe neuron.
For the convenience of description, we first consider the case that the bump height A r ( t ) has littlevariation during the bump oscillation (for other situations, see Sec. 4).
In such case, variations ofthe firing rate of the probe neuron is determined by the variations in h ( t ) , which is composed of afunnel-shaped signal v ext t , and a sinusoidal signal c 0 sin ωt + d 0 whose amplitude is far less thanthe firing field of the probe neuron ( c 0 ≪ a , see SI.3 for the derivation of c 0 ).
As the oscillationfrequency is also much quicker than the moving speed, the sin wave can be seen as a signal beingsuperposed on the funnel-shaped signal.
This naturally gives the envelope of the firing rate to be ofthe waxing-and-waning shape, which is observed in the experimental data as the animal traversed thefiring field of a place cell (Fig.4B bottom) [9, 10].
We further study the firing phase of the probe neuron in each theta cycle, which is reflected by themoment when the neuronal response reaches a peak in a theta cycle.
From Eq.(10), we see that thispeak firing rate is achieved when the absolute value of the displacement | h ( t ) | reached the minimum value in each theta cycle
We distinguish three scenarios of the firing phase below (Fig.4B&C):
• Fixed entry phase .
When the animal just enters the place field of the probe neuron, the locationof the probe neuron is far away from the bump center, i.e., h ( t ) < 0 always holds.
The minimumvalue of | h ( t ) | in a theta cycle is reached when c 0 sin( ωt ) =
c 0 .
This gives the entry phase as afixed value of ϕ = ωt = π/ 2 .
• Phase precession and procession .
As the animal approaches the center of the place field, i.e., inthe range that − c 0 − d 0 < v ext t < c 0 − d 0 , the firing peak of the probe neuron is achieved whenh ( t ) = 0 .
This gives two solutions of the phase for peak firing as follows:
[Equation]
with ϕ f occurring in the forward propagation of the network bump (forward theta sequences), andϕ r occurring in the reverse propagation of the network bump (reverse theta sequences) (Fig.4C
upper two panels).
As the animal travels through the place field of the probe neuron, v ext tincreases from ( − c 0 − d 0 ) to ( c 0 − d 0 ) .
This leads to ϕ f decreasing from π/ 2 to − π/ 2 , and ϕ rincreasing from π/ 2 to 3 π/ 2 , resulting in phase precession and procession, respectively.• Fixed departure phase .
When the animal is about to leave the place field of the probe neuron,h ( t ) > 0 always holds.
The minimum value of | h ( t ) | is reached in a theta cycle when c 0 sin( ωt ) =− c 0 , and this gives the departure phase as a fixed value of ϕ = ωt = − π/ 2 (Fig.4C
bottompanel).
Combing the above results, we see that as the animal traverses the place field, the probe neuron exhibitsboth phase precession and procession, and they occur in the forward and reverse theta sequences,respectively (i.e., in the forward and reverse propagation of the bump oscillation, respectively).
Notably, our model also predicts a fixed entry phase as pointed out by the experimental data [9, 10](note that the exact value of the entry phase is not important, as it depends on the reference point).
Feedback inhibition strength accounts for the emergence of bimodal cellsand unimodal cells
In the above analysis, we have shown that under the interplay between external drive and feedbackinhibition, neurons in the CANN exhibit both significant phase precession and procession in individualtheta cycles, with the former determined by the peak firing time in the forward bump propagation and
[Figure]
the later determined by the peak firing time in the backward bump propagation.
Place cells in thehippocampus having this property are termed as bimodal cells [27].
In fact, previous experimentshave already identified another type of place cells which only exhibit phase precession when theanimal moving through the corresponding firing field [9, 10], and they are termed as unimodal cells.
From the view of population decoding, these unimodal cells contain only forward sweeps of decodedposition.
There are compelling evidences that these two types of place cells participate differently inthe encoding of spatial information.
While the unimodal cells may exclusively represent possiblefuture outcomes, the bimodal cells could also represent prior behavior in the reverse order.
Here weshow that by varying the feedback inhibition strength, our model can explain the emergence of bothtypes of place cells discovered in the experiments.
For the simplicity of analysis in Sec. 3, we assumed that the bump height A r ( t ) (also, A U ( t ) ) haslittle variation during bump oscillation.
In practice, this is only true when the feedback strength mis relatively small.
From the solution of the oscillation amplitude c 0 (see eqn.
(70) in SI.3), we seethat c 0 scales with m in a sublinear way.
When m is small, the intrinsic mobility is small, and thebump is more anchored by the external drive than the intrinsic mobility, leading to a small oscillationamplitude.
Because the height of the external bump is not changing across time, the network bumpwill accordingly have little variation in the height (Fig.
5A upper panel).
Therefore, neurons in the
CANN have both significant firing peaks in forward sweeps and backward sweeps (following theanalysis in Sec. 3), and exhibit the property of bimodal cells.
While, when m is large, the intrinsicmobility becomes large, and the bump is less anchored by the external drive, leading to a largeoscillation amplitude.
As the internal bump oscillates to the location far from the external bump, thebump height starts to attenuate due to the weak external drive at that location.
Since the feedbackinhibition is a much slower process compared to the neuronal response ( τ v ≫ τ ), the bump heightwill keep attenuating till it sweeps backward to the location of the external bump (Fig.
5A lowerpanel, also see the video demonstration in SI).
This backward attenuation causes the firing peakduring the backward sweep no longer significant, and hence the probe neuron appear to elicit onlya single firing peak during the forward sweep in individual theta cycles (Fig. 5B), exhibiting theproperty of unimodal cells.
We examine the phase shift behaviors of neurons in the network by varying the feedback inhibitionstrength.
To compare our simulation results with the experimental data, we follow the same process.
The simulation results show that: 1) when m is relatively small ( m = 3 .
125 , see SI.1 for all parametersettings), all neurons in the CANN are bimodal cells, which exhibit both significant phase precessionand procession (Fig.
5C upper panel); 2) when m is relatively large ( m = 3 . 15 ), all neurons in the CANN are unimodal cells, which only exhibit significant phase precession (Fig.
5C lower panel).
Notably, unimodal cells in our model also display a weak effect of phase procession (although bump height attenuates, they can still generate minor peak firings sometimes), although it is not assignificant as that in bimodal cells.
This is consistent with the experimental findings (see Fig.2 in
SI.4), indicating that phase procession is a general property of hippocampal place cells [27].
Conclusions and Discussions
In the present study, we have proposed a continuous attractor neural network with feedback inhibitionto elucidate the generation of theta phase shift of hippocampal place cells during animals’ locomotion.
We show that the interplay between the intrinsic mobility (arising from the feedback inhibition) andthe extrinsic mobility (arising from the external drive) leads to the oscillatory tracking behavior ofthe network, which naturally accounts for the forward and backward sweeps of the decoded position(around the physical position) when the animal moves freely on a linear track.
At the individualneuron level, the forward and backward sweeps of the network bump account for, respectively, thetheta phase precession and procession of individual place cells.
We also show that by tuning thefeedback inhibition strength, neurons in the network can exhibit the property of either bimodal orunimodal cells, with the former having co-existed phase precession and procession in individualtheta cycles, and the latter having only significant phase precession.
Oscillatory tracking in attractornetworks has been studied previously [52, 53, 54], but these works have not explored its biologicalimplications.
To our knowledge, our work is the first one that formally links oscillatory tracking tophase shift of place cells.
Previous modeling works have mainly focused on the generation of theta phase precession in placecell firing, and these models can be divided into two categories, with one focusing on the mechanismof single cell oscillation [9, 30, 28, 29, 31] and the other on the mechanism of recurrent interactionsbetween neurons [32, 33, 34].
A representative model of the former is the dual oscillator model [9, 30],which produces phase precession via the interaction between two oscillatory signals of differentfrequency.
One signal represents the baseline somatic oscillation and the other with a slightly higherfrequency represents the dendritic oscillation, and the superposition of two signals leads to that thefiring peak of the cell progresses in successive theta cycles.
A representative model of the latter isthe spreading activation model [32], which produces phase precession as a result of the asymmetricpropagation of neural activity along the motion trajectory of the animal, caused by asymmetricsynaptic interactions.
It is noteworthy that these two different kinds of models need not to be mutuallyexclusive, as each of them explains some aspects of the phase precession behavior [55].
Comparingwith previous works, our model has two novel contributions: 1) explaining the co-existence of phaseprecession and procession, while previous models explained only phase precession; 2) elucidating themechanism (via tuning the feedback inhibition strength) of generating bimodal and unimodal cells,which was not considered in previous models.
Moreover, we carried out comprehensive analysis ofthe network dynamics to unveil the underlying neural mechanisms clearly.
The feedback inhibition plays an indispensable role in our model.
It should be emphasized that thesimplified feedback inhibition form in our model does not mean a direct reciprocal connection betweenthe pyramidal neurons (place cells) in the hippocampus (HPC) and the GABAergic neurons in themedial septum (MS).
In fact, there is not direct projection between these two neuron populations [40,41, 56, 57].
Instead, the only feedback pathway between the HPC and the MS arises from reciprocalprojections between the GABAergic (CaBP-containing) neurons in the HPC and the GABAergic(PV-containing) neurons in the MS [40].
Since the GABAergic (CaBP-containing) neurons receiveconvergent excitatory inputs from the pyramidal neurons (place cells) in the HPC, a possible wayof realizing the effect of feedback inhibition could arise from the complex interactions among thepyramidal neurons and GABAergic (CaBP-containing) neurons in the HPC, and the GABAergic(PV-containing) neurons in the MS.
Moreover, the feedback inhibition may have layer-specificeffects on neurons in the HPC pyramidal layer.
Since bimodal cells have firing patterns similar toneurons in the deep HPC pyramidal layer while unimodal cells are more similar to neurons in thesuperficial layer [27, 58], we hypothesize that neurons in the deep HPC pyramidal layer may receivea larger feedback inhibition effect than neurons in the superficial layer, leading to the differentiationof unimodal and bimodal cells.
In the future work, we will extend the current model to includemore detailed biological structures accounting for the realizations of feedback inhibition and otherproperties in the CANN.
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(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?
[N/A]
(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?
[N/A]