![[Goal Distance Dependent Firing]](goal-distance-dependent-firing.png)
(goal-distance-dependent-firing.fig)
This is a log of experiments conducted using the Catacomb simulation environment to test models of brain function in behaving animals, most commonly simulated rats.
A list of all Catacomb models in the virtual rat project: ~/src/nnmodels/ccmb/*.ccm*
|
Figure eight causes diagonals to be learned as well... this may be avoided by setting the plastmodthreshold (LTP threshold) on ECIII recurrent to 70% and by modifying their transmod function to have a phase of -40. These changes should help to disambiguate the encoding and retrieval phases of the network.
Doing this helped somewhat, but some undesired weights are still established. This happens once a complete circuit of the figure eight is completed. As activity returns to the orginal location, the cell at the top of the stem is reactivated and becomes associated with a cell at the bottom of the right-hand loop. Subsequently, as the rat begins the reverse traversal, other cells are associated in that manner.
[local-connectivity]This could be avoided entirely by having only local connectivity.
The first instance of trouble is around t=4160. Spiking of the cell at the bottom of the stem seems to recall the cells along the stem, which are subsequently associated with recently active cells. This all happens during the encoding phase. It is not related to the goal signal, which only appears in the retrieval phase.
The retrieval of the other cells in the stem should not be happening during the encoding phase (low theta), despite the level of ADP (which ECIII here does not even have) or other factors.
[transfer-modulation]Another obvious way to avoid retrieval during the encoding phase is to utilize GABA_B receptor modulation of recurrent synapses.
Look at the effect the transmod function has in ECIII. Check to see where activity occurs in comparison to that function. See how the function should be adjusted in order to properly suppress recurrent retrieval during encoding. It may yet be possible to add direct modulation of membrane potentials.
The falsely recalled ECIII activity in the stem occurs in the retrieval phase of the transmod function with phase offset -40. That is as desired, in that the transmod function should impose the mode on the recurrent synapses. Unfortunately, the peak of the retrieveoscneg40 function is very near the peak of the encodeosc14 function that is to link the activity of consecutive locations by modulating the afferent activity from ECIIcanm to ECIII. The previous function, RetrieveOscPos166, seems to have a much more orthogonal phase to that of the encoding function. So why was it replaced with -40? Setting the original function caused even earlier undesired connections to appear, since the phase was such that retrieval occurred at the top of the right-hand circle while encoding was going on at the bottom of that same circle.
Setting plastmodthreshold to 80 percent removed most of the unwanted connectivity.
[dendritic-modulation]Using a real dual-compartment model, or an approximation created by linking one cell body integrator compartment to another with a tube, dendritic function can be separated from cell body function. That allows an entire dendritic section to be modulated out of phase with the cell body, which can act as an all-or-nothing mode control. Recurrent synapses connected to the dendritic compartment can be effectively silenced when the dendritic compartment is modulated GABAergically.
From investigations of the cell activity in PFC, ECIII, CA3 and CA1, it is clear that multiple paths are simultaneously suggested, which causes the undecided behaviour of the rat. Even a random delay between transmissions from one cell to another could possibly avoid this. It is worth trying from a different initial position.
Moving from -40 to -50 for the retrieval oscillation helped somewhat, since starting from the middle of the stem (asymmetric with regard to the goal) again caused a few diagonals to appear. Diagonals were completely abolished by setting the maximum conductance that ECIII weights could achieved through LTP to 16.0 rather than 20.0. Unfortunately, that also led to a lack of retrieval, so that the rat did not move from its position when "run net" was attempted after training.
This may be achieved in approximation right now by attaching an interneuron to ECIII that is driven by EncodeOscNeg14 or by attaching a hyperpolarizing theta oscillation at the same phase. The afferents from ECIIcanm must be sufficiently strong to cause spiking despite that theta modulation of the ECIII membrane potentials.
In the model figure-eight-theta.ccm, I have now added the stimulation node ECIIItheta, with the oscillating signal ThetaHypEC, which is modeled after the signal ThetaDepolEC, and about 180 degrees out of phase with the EncodeOscNeg14 transmod function. It will therefore provide inhibition during the high phase of encoding and excitation during the low phase of encoding. The conductance from the stimulus node, the conductance from ECIIcanm, and the maximum conductance that can be achieved by recurrents in ECIII must now be designed to work together. One way to do this is to first lower the recurrent maximum conductances quite a bit and concentrate only on making encoding work with the new ECIIItheta stimulation included. Then retrieval can be added.
To do this, I have now created the ECIIILTPparameters, in which the maximum conductance has temporarily been reduced to a tenth of its former value, namely 2.07.
I then reduced the conductance from the stimulation node to ECIII from 4.0 to 3.0 and increased the afferent conductance from ECIIcanm to ECIII from 20.7 to 30.0.
Reducing the plastmod threshold now should help by allowing learning to proceed more easily while retrieval is disabled. I have now set the plastmod threshold on ECIII recurrents to 50 percent.
ECIII recurrents : E=0, Gmax=10.07, delay=2.12, Trise=1, Tfall=2 ECIIcanm afferents: E=0, G=40, delay=1, Trise=1, Tfall=2 ECIIItheta : Emax=-30, Emin=-92, G=3, frequency=8The rat seems to learn the track well now. I may wish to set the transmod function back to RetrieveOscPos166 if the addition of theta modulation in the membrane potential suffices to disambiguate encoding and retrieval. Logically, the transmod and plastmod functions should be 180 degrees out of phase, so if the transmod function is set back to RetrieveOscPos166, then the plastmod function should be EncodeOscNeg14. Interestingly, the name of the transmod function implies that phase, but does not actually implement it. Instead, it appears to implement a phase near 0. That may simply be a later (debugging) setting by Mike. It is perhaps a good idea to set that back to -14 as well. [plasticity-modulation]Note though that the plastmod function should not be necessary if the model is working robustly, unless there is actual physiological cause to believe that plasticity is modulated in such a manner.
Spiking throughout ECIII appears to fall within the high portion of the encoding signal (although some minor shifting may be possible to center activity at the peak more precisely). The only exception is the additional spiking of the goal location in ECIII, driven by periodic PFC spiking.
The encoding phase appears to be working properly with the new ECIIItheta modulation. Now the retrieval phase must be brought back online.
I'm setting ECIII recurrent Gmax to 20 as a test.
That was too strong, as all diagonals were again added. Either the recurrents must be sufficient at a lower Gmax value, or the conductance from ECIIItheta must be increased. ECIII output is of the proper strength, but the spikes must occur as desired. During encoding, only encoding spikes should occur. During retrieval, ECIII must be able to propagate retrieval through its recurrents. I must test retrieval with "run net" to determine the necessary modification ((a) ECIII recurrent Gmax around 10 or (b) stronger ECIIItheta).
I have set Gmax back to 10 and follow training with "run net".
Inspection of the "run net" result, in which the rat remained stationary, indicates that ECIII spikes at the rat's location occur during the trough of the retrieval signal. That means that the transmission of the spikes is inhibited by the transmod function. ECIII is supposed to implement (controversial) backward propagation of spikes from the goal location, which is driven by PFC. The goal activity still occurs properly near the peak of the retrieval signal, where the transmod function allows maximal transmission through recurrents and the ECIIItheta signal produces minimal inhibition. The recurrent conductances may need to have a greater Gmax. A possible way to do this, while retaining clean encoding is:
I am testing a greater ECIIItheta amplitude by increasing the conductanve of the signal to G=5.
Some diagonal encoding reappeared. Retrieval and encoding were again insufficiently distinct.
I'm temporarily setting G of ECIIItheta back to 3 for clean encoding.
Tuning Distinct Mode Controls
Means to achieve distinct training and navigation stages:
The issue marked (*) was problematic upon inspection after training with ECIIItheta conductance G>3. As ECIII cells were more distant from the goal location, their turn in the chain of retrieval appeared later. Retrieval spikes for some cells therefore occurred during the encoding phase. Once that occurs, attempts to distinguish training and navigation phases by methods such as avoiding associations across phases in (a) are powerless. Operations (e.g. learning) that take place in particular phases can only be designated to act on spikes in that specific phase, if the phases and their spikes do not overlap.
Propagation using subthreshold signals
Some further effort is required when the number of inputs that converge on a cell is not known in advance, such as when multi-cell patterns are used to represent a location or knowledge item. In that case, the maximum recurrent conductance achieved by LTP may need to be adaptable, set perhaps to the connectivity (i.e. sparseness) of patterns.
With the current back-propagation approach, the additional concern is also raised to deal with equidistant cells that receive converging input from multiple paths. A solution for this is presented for the most reliable of the signaling methods discussed below.
Here follows the result that is to be achieved and a number of propagated signal codes that can be used.
The desired result:
Types of signals:
An example using code E:
Cell 6 in the example above exerts a greater pull by spiking more rapidly than cell 4, despite the equidistant location of cell 4 relative to the goal. As each ECIII place cell must receive three recurrent spikes to activate in a retrieval phase, the decrease in activity is exponential with distance. The exponential nature of the decrease outweighs any summation of activity from converging inputs.
The number of spikes needed for activation can be tuned to adjust the robustness of the code in the presence of noise that can change spike timing along various paths. It is not desirable that many spikes are needed, as that slows down propagation. An alternative that maintains strong reliability is to filter inputs (although that would require a modification of the architecture). Each ECIII place cell would receive recurrent input only from a corresponding filter cell. The filter cell would receive recurrent inputs from other ECIII cells, responding with only a single spike per discretization time unit (due to a strong AHP). Thus any number of spikes received in the same discretization time unit are interpreted as a single spike.
It is also possible to suppress activity in the current location in ECIII, which would avoid propagation through that location to equidistant place cells in a loop. Notice that such suppression is not a general solution, because other equidistant locations can exist in loops that don't intersect the current location.
Once the goal information has propagated to the current location, all ensuing steps can happen quite rapidly, even with code E. The most rapid implementation is computed as follows:
The new ECIIinput population has been designed to have AMPA synapses with a fall time of $\tau_{fall}=4$ ms and conductance $G=5$, so that the effect on membrane potential due to only the place input from the feature discretizer is an elevation to $V=-58$ mV for cells corresponding to place fields that the virtual rat is in. This predisposes those cells to fire when receiving spikes from ECIII. The transmission modulation function alone does not do very much to avoid spiking in the ECII buffer in a particular phase, since responses are slow and prior contributions can suffice combined with even a small transmission to achieve spiking. The addition of the membrane potential modulation should complement this to achieve the desired effect.
New Direction:
Instead of reimplementing the ECII buffer as it was, a new implementation is made, using the 3-4 item STM buffer model based on dual oscillations. The aim is to reimplement, while correcting older limitations of the model. The improvements are:
Theta modulation:
In order to achieve a sinusoidal theta modulation of the membrane potential between -65 mV and -55 mV, it was necessary to set the conductance of the clamp to 980, given a generated signal between -70 mV and -50 mV at 6.3 Hz. These values may be somewhat different for a signal with a frequency of 8 Hz.
Instead of using a sinusoidal function to approximate theta oscillations, theta stimulation can be modeled as a combination of depolarization caused by reduced K+ leak current and periodic responses to strong inhibition caused by a network of interneurons with GABA_B synaptic channel connections to the pyramidal cell body.
The depolarization due to reduced K+ leak current is implemented by changing the pyramidal cell's resting potential to $-53$ mV. (The reset potential may also be moved from -60 to -53 mV.)
The amplitude of the inhibitory response is assumed to be $-10.5$ mV. The rise and fall times of the synaptic response function are set to emulate a rapid hyperpolarization with a return to resting potential according to $((t-t_{fire})/\tau_{GABA_B})\exp(1-(t-t_{fire})/\tau_{GABA_B})$ , where $\tau_{GABA_B}=30$. This was achieved for a pyramidal cell with $T_{leak}=50$ ms, using the synaptic parameters $G=900$, $E=-90$ mV, $T_{rise}=0.001$ ms, $T_{fall}=30$ ms. (Note that the conductance and potential differences are very similar to those of the clamped sinusoidal signal, G=980 and voltage between -70 mV and -50 mV.)
An alternative set of parameters that produces a theta modulation based on $GABA_B$ channel responses with the same amplitude, but a steeper positive flank is: $G=1150$, $T_{fall}=20$ ms, $V_{rest}=-53.5$ mV.
Modifications of the STM network:
The current modifications that needed to be applied seem to be pushing the STM network into a realm with much greater conductances. Theta modulation through GABA_B dynamics required conductances of 900, and the induction of spiking by afferent input during a low theta mode required a conductance of 1250 with $E=20$ mV, $T_[rise]=2$ ms and $T_{fall}=5$ ms. To achieve repetition of the spike, the ADP conductance was raised from the original 3 to 400! It is not yet entirely clear why this escalation is taking place. The cell's capacitance may be involved, or it may be the result of a general change in the equivalent electrical network caused by the different delivery of theta modulation. With these values, proper behaviour is not yet achieved, since consecutive items in STM merge.
Issues/Bugs awaiting resolution:
Changes since the above (20020110): (1) Laplace transformations are now being used to determine analytically how operational criteria can be specified. (Figure: neuronal-balance-calculations.fig) (2) The conductances have been standardized to nS. This breaks all previous models, and requires significant adjustments to the STM model and other parts of the new implementation. (3) Since changes were needed anyway, the STM model is being adjusted to work with the local theta frequency (8 Hz) and the pyramidal resting potential chosen here (-70 mV rather than -60 mV). A good system for the implementation of the STM model should be independent of the choice of such parameters in any case.
ADP and theta slopes: As long as the ADP responses of consecutive memory items are similar and therefore parallel, separation is best maintained when the response to theta is as flat as possible near the positive peak of theta (with an assumption of additive properties for theta and ADP). Hence, a theta modulation generated synaptically is most beneficial if it has fairly rapid fall timing characteristics, yet sufficient conductance to enforce theta cycles strongly. An example of appropriate parameters may be synaptic reversal potential $E=-90$ mV, characteristic fall timing $\tau_{fall}=2$ ms and conductance $G=200$ nS.
Criteria for a STM buffer recipe: Once the Laplace results for stability criteria are known, a recipe for this STM model design can include specification of the theta synapse. In order to specify a proper theta modulation, the parameters that must be taken into account are: resting potential in the target population pyramidal cells, $V_{rest}$ (e.g. -70 mV), the threshold potential, $V_{thres}$ (e.g. -50 mV), the desired theta amplitude (e.g. 10 mV for modulation between -80 mV and -60 mV), the theta frequency, $f_{theta}$ (e.g. 8 Hz), the leak conductance in the target cells, $G_{leak}$. There may be more. Parameters, such as the adjusted resting potential in target cells, the theta synapse conductance and characteristic timing can then be calculated accordingly. Dependencies propagate from there, e.g. interneuronal spike timing may be adjusted to achieve a number of gamma periods in the positive portion of a theta period.
Theta implementation: With rise timing $\tau_{rise}=0.01$ ms, a combination of fall timing $\tau_{fall}=2$ ms and conductance $G=240$ nS achieves a slope in which theta rises 10 mV in 85 ms in the positive portion of theta. With a combination of fall timing $\tau_{fall}=1$ ms and conductance $G=480$ nS that slope is 10 mV in 88 ms. The two slopes are very similar, so both combinations are usable.
Afferent input implementation: With the new theta input, afferent input is properly received (at least if presented in an encoding phase) with typical AMPA timing characteristics ($\tau_{rise}=1$ ms and $\tau_{fall}=2$ ms), excitatory AMPA reversal potential $E=0$ mV. Afferent spikes are achieved and multiple spikes or bursts avoided with synaptic conductance amplitudes between $G=40$ nS and $G=100$ nS.
Pyramidal AHP implementation: It is not quite clear yet, how strong the AHP should be. The AHP should probably avoid multiple spikes, therefore it should have a rapid onset, $\tau_{rise}=0.0001$ ms, immediately following the absolute refractory period of 2 ms. It should probably also inhibit multiple spiking within a theta period, unless achieved with the aid of the recurrent excitatory activity of an overlapping memory pattern. For this reason, it's fall time is currently relatively long, $\tau_{fall}$ between 5 ms and 10 ms. If its reversal potential is similar to that of inhibitory input, it can be set to $E=-90$ mV. With these values, the conductance can be between $G=200$ nS and $G=800$ nS.
ADP implementation: The ADP is properly achieved with $E=-10$ mV, $G=10$ nS, $\tau_{rise}=800$ ms, $\tau_{fall}=1$ ms and a duration of 125 ms. The conservative setting of the duration parameter avoids superposition of ADP onto subsequent theta cycles, which is probably physiologically plausible. The ADP parameters may need to be adjusted if physiological reasons warrant it.
Operation of STM buffer based only on ADP: With the settings above, repetition of afferent input during the retrieval portion of each theta cycle is achieved. Different items do still merge after about three theta cycles of separate coexistance, which may be sufficient for the purposes of this model. So that the implementation of the STM buffer model is satisfactory, the recurrent GABAergic inhibition is attached for the generation of gamma cycles.
Interneuronal network for gamma oscillations: The interneuronal network node is currently set up with an AMPA input ($\tau_{rise}=1$ ms and $\tau_{fall}=2$ ms) with conductance $G=30$ nS, which causes the node to spike (the conductance is twice the leak conductance of the interneurons with $r=35$ micron and $\tau_{int}=10$ ms). The AMPA input is not too strong, so that multiple gamma spikes can be avoided through the interneuronal AHP. That AHP is set to $E=-90$ mV, $G=200$ nS, $\tau_{rise}=0.0001$ ms and $\tau_{fall}=7$ ms, with a duration of 20 ms (so that the AHP will not be superimposed on a subsequent gamma period). These parameters may need to be adjusted if the gamma cycles do not cooperate satisfactorily with the theta cycles.
Dynamic requirements: There is an issue concerning the desired strength and dynamics of gamma contributions and the time constant of the pyramidal cell membrance capacitance in the STM buffer. The current setting of $\tau_{pyr}=50$ ms limits the rapidity of response to gamma dynamics. That implies that gamma responses can be only either of small amplitude with a small period (the desired 20 to 25 ms) or of large amplitude (as may be needed for adequate separation of gamma periods) with a greater period (which allows too few gamma periods to exist in the positive portion of a theta cycle). For this reason, it may be necessary to speed up the pyramidal dynamics.
Updated Pyramidal dynamics: A basis for an updated pyramidal cell may be physiological characteristics (such as those at http://neuron.princeton.edu/~mol437/references/brain.ps). A human pyramidal cell can have a typical radius of about 20 micon. Leak conductance can be estimated (an example is at http://www.cnbc.cmu.edu/~bard/synapse/node1.html), e.g. with $0.1 mS / cm^2$. Here, the leak conductance is kept at approximately its former value (to minimize necessary adjustments in other parameters), $G_{leak}=6.1$, by setting the radius to the plausible value of 22 micon and the time constant to $\tau_{pyr}=10$ ms. With these settings and a conductance from the interneuronal network to each pyramidal cell of $G=50$ nS, the GABAergic in hibition in gamma cycles can achieve a hyperpolarization of about 10mV in a resting pyramidal cell, which returns to $V_{rest}$ within the gamma period. (Similar useful pyramidal parameter settings are $r=22$ micron and $\tau_{pyr}=8$ ms, which lead to $G_{leak}=6.28$ nS.)
Parameters adjusted for new dynamics: An additional benefit of the faster pyramidal dynamics is the ability to more precisely control the theta response. It is fairly easy to specify a synapse fall timing that allows potentials to return to the resting potential, so that a K+ modified resting potential of -60 mV can be specified. The flatness of the positive portion of theta (which can be a proportionate majority of the theta period) can be adjusted between very flat (for theta timing characteristics $\tau_{fall}=10$ ms) to gently sloped ($\tau_{fall}=14$ ms) or more steeply sloped to compress consecutive spikes ($\tau_{fall}=20$ ms). Using the gentle slope, the desired theta amplitude of 20 mV is achieved with a conductance $G=22$ nS. Single afferent spikes are maintained with an afferent conductance modified to between $G=15$ nS and $G=20$ nS, although a much broader range is acceptable if absolute avoidance of double spikes is not a great priority. The AHP was adjusted to $\tau_{fall}=15$ ms (duration $100$ ms so that it is computed for the entire theta period following a spike) with a conductance between $G=50$ nS and $G=400$ nS, although a broader range of parameter values may also be applicable if such becomes a functional requirements of the AHP. The ADP conductance was modified between $G=6$ nS and $G=10$ nS (for maximal usage of the positive portion of theta, $G=12$ nS already causes some items to fire twice in a theta cycle, once at the very beginning of the positive portion and once at its end).
Gamma cycles: The interneuronal output is connected to the pyramidal cells of the STM buffer via synapses with $E=-70$ mV, $\tau_{rise}=1$ ms, $\tau_{fall}=5$ ms and a conductance $G=20$ nS. The STM buffer maintains two items in the order of their presentation for about 500 ms (four theta cycles). The items decay and are consequently lost from the STM buffer in their order of presentation. Each item spikes 7-8 times. By increasing the ADP duration from 125 ms to 150 ms the decay problem was solved. Apparently, the continual shifting to earlier onset times during the positive portion of theta caused the decay - the ADP did not span the necessary duration to achieve spiking in a subsequent theta period. The STM buffer now maintains two items in their proper order in consecutive gamma cycles of each theta cycle indefinitely!
The STM buffer can also hold three items in their proper order for a limited amount of time, but needs some further adjustment so that it can do so indefinitely.
STM buffer input: Information arriving at the STM buffer should be filtered, so that approximately one new afferent item is presented per theta cycle. Both ECIIinput and the STM buffer in EC receive input directly from place activity (generated by a FeatureDiscretizer concatenated with a SpikeSplitter object). The place activity is regular (at 50 Hz). The ECIIinput population will be adjusted so that a single spike occurs for each burst of place activity, while the STM buffer should spike at the retrieval phase of each theta cycle. The afferent place input should be presented during the encoding phase of the theta cycle, with a sufficient AHP. If repeated presentation threatens to flush the buffer before subsequent places can be associated, then presentation should not occur on each encoding phase, but only on those where novel inputs are received (a new location is entered). This remains to be seen, but can be accomplished with a feedback loop that modifies presentation strength according to novelty.
In its current condition, the STM buffer may already achieve its goals with regard to the needs of the current model, even without further filtering of the input. The AHP already appears to be strong enough to limit spiking to one spike per item per theta cycle. Neither the maintenance of order, the effect of multiple presentations of the same place input, or the timing of afferent input can be guaranteed at this time, it does appear that successive place input is repeated in sufficient temporal proximity to allow LTP to occur. This is adequate as long as bidirectional connections are permitted in path learning.
Immediate STM buffer objectives:
Issues with the ECII input population: (a) Why do all cells appear to spike once at t=0 ms? (b) Cells should spike only in the presence of sufficient place input and ECIII input. Issue (b) is taken care of by modifying the conductance of the input synapses by the factor 100 that reflects that change in units. With $G=0.05$ nS, the proper behaviour is achieved, except that ECIII output may still be incorrect.
Issues with ECIII output: The first task is to get ECIII to follow the information coming from the STM buffer in ECII. This is also an opportunity to take some of the parameter variations out of the model and to standardize on some concrete types of neurons. The ECIII neurons are made to correspond with the model of entorhinal pyramidal cells used in the STM buffer, with the aim that their behaviour is a predefined response to theta modulation and gamma cycles. The clamp is removed, so that the more biologically plausible synaptically induced theta can be added when desired. The AHP is modified to resemble that used in the ECII STM buffer. The theta and gamma synapses correspond to those in the STM buffer, while the cell is recalibrated ($V_{rest}=V_{reset}=-60$ mV, $r=22$ micron, $\tau_{pyr}=10$ ms) so that theta can modulate membrane potential around an average of -70 mV. LTP is temporarily deactivated by setting $G_{max}=G$. This can help to achieve the desired behaviour induced by input from the STM buffer. That input is given a conductance $G=15$ nS. This achieved ECIII spiking that follows ECII STM buffer spiking perfectly.
ECIII learning and ECII input buffer behaviour: When LTP is activated by setting $G_{max}=15$ nS in ECIII, autoassociative learning does occur as expected. Unfortunately, item repetitions in the ECII STM buffer are as yet continuous, so that eventually all cells become associated. The ECIIinput population is corrected by adding a seperate synapse for ECIII input, with stronger conductance $G=0.15$ nS. This produced the desired ECII input population behaviour, with a single spike where place input and ECIII input occur together.
STM buffer slow AHP: To limit the duration of STM repetition, a functional slow AHP is added. Currently, a simple way to add this is through an additional synapse in the STM buffer ($E=-70$ mV, $G=0.5$ nS, $\tau_{rise}=800$ ms, $\tau_{fall}=10$ ms, duration=1200 ms) and a network pathway with one-to-one connections from the buffer output to that synapse. This implementation is used, since response functions (such as the fast AHP and ADP responses) are by definition reset at each spike, while the function governing the shut-off of item repetition must act over multiple spikes. The network pathway connection object cannot (currently) be captured within a neuron object, hence it is connected externally (delay=1 ms). By setting $G=0$ on the slow AHP synapse, the buffer can operate in the indefinitely repetitive mode. The chosen conductance allows an item to be repeated for 7 to 9 theta cycles, approximately 800 to 1000 ms. Some precision issues remain with the STM buffer, in addition to the points noted above: (1) As the first two place inputs appear, they are not kept in their order of presentation. (2) Some new input appears to spike more than three times during the first theta cycle (the first spike may actually appear at the very end of the previous theta cycle). (3) As the virtual rat traverses the path backward, STM buffer cells in those locations are still suppressed to some degree by the slow AHP (perhaps the slow AHP should be turned off completely once repetition has stopped). The slow AHP should probably also turn off repetition more rapidly, after 3 theta cycles for instance.
Sequence Learning: The STM buffer needs to be adjusted to solve (3) above - a transmission modulation in the afferents may suffice. Another interesting modification may be to give afferents slow dynamics, but have them be subthreshold during the encoding phase. That way, the STM buffer would not spike for afferent input, so neither would ECIII. Preferably, the order should also be retained in the STM buffer (with adequate flushing of older items). Learning in ECIII and CA3 should be primarily heteroassociative (changing the onset of the LTP function may help, see papers about LTP including the author Poo from 1998), and should convey the sequence order by binding only consecutive items. Since a ``Cumulative Response'' object is now available in Catacomb, I am replacing the improvised slow AHP circuitry with that. The cumulative slow AHP is tested with the parameters $E=-70$ mV, $G=1$ nS, $\tau_{rise}=400$ ms, $\tau_{fall}=10$ ms and duration=400 ms. Some adjustements will be necessary, once the afferent input has been regulated, to produce the desired effect in the STM buffer.
Sequence Learning - cleaning up STM: I am adjusting the slow AHP and adding transmission modulation to deal with point (3) above. While it is desirable that the transmission modulation on recurrent collateral synapses follows the membrane potential modulation caused by theta oscillations, the transmission modulation on afferent input should allow afferent spiking in only a very restricted portion of the theta cycle. To achieve this, the GABA_B receptor modulation of afferent terminal transmission was rescaled so that a broader period of suppression resulted. By combining such transmission modulation with a slow afferent synaptic response, arbitrary spike arrival times can be modulated to approach desired synchronization. This is a model for the stages leading from arbitrary sensory spike timing to synchronous processing in theta cycles. Synchronicity can be refined as spikes propagate through multiple layers of excitatory cells with theta modulated membrane potentials and afferent synaptic transmission. (Of course this can also be done using consecutive layers with transmission modulation in phase with membrane potential modulation.) This approach appears to be able to solve point (2) above as well. (Note that the rescaling is currently off, as the quality of the spiking on the first cell of the STM buffer appeared to be almost the same with or without rescaling.) Lowering of the afferent conductance to 10 nS resulted in a cleaner sequence memory for spikes on the first to place cells, but spiking still occurs during the encoding period and the first spike of the second place field still falls on the end of a retrieval phase of a theta period. The desired transmission modulation function for afferents to the STM buffer is achieved by reversing the rescaling, so that the function is a mirror image of the membrane theta modulation. But is there a plausible physiological way for such a function to appear at the terminals of afferent fibres? And... why do the second place cell's spikes no longer achieve STM buffer spiking?
Goal Activity: In order to achieve the effect of goal activity in ECIII, three things must be verified: (1) Heteroassociative pairs must be maintained in the STM-buffer. (2) A strengthening of synaptic efficacies must take place between consecutively active cells in an episode in ECIII. (3) The goal location must activate and periodically reactivate in PFC as a result of the combination of place activity and the discovery of the goal. Then the activity of the goal can retrieve episodes in ECIII through backwards spread. The PFC population is implemented in a similar manner as the STM-buffer population, but without interneuronal network input to create gamma cycles and without a slow AHP, so that repetition is indefinite. Two synaptic populations are provided for afferent input, one from the goal detection signal and the other from place input. The conductance from place input is set to $G=3$ nS, so that activity remains just below threshold in the absence of a goal detection signal. The conductance of the proximity signal (from the ingester component) was set to $G=2$ nS, so that its response also remains below theshold in the absence of place input. Where the proximity signal and place input combine, spiking is induced. That spiking is repeated indefinitely, once on each theta cycle. By increasing the conductance on afferents from the STM-buffer to ECIII to $G=25$ nS, all spikes in the STM-buffer are properly conveyed. It is possible to set the conductance of the STM-buffer's slow-AHP to $G=1.1$ nS, so that the first and second place field spikes co-occur closely for an extended period of time. A better solution would be to have the first place field spike occur earlier in its second theta cycle, so that the second one can spike in the proper order. This better solution is initiated by raiding the ADP conductance in the STM-buffer from $G=8$ nS to $G=10$ nS. This is still within the range advised above (between $G=6$ nS and $G=10$ nS). I then increased the slow-AHP conductance to $G=1.8$ nS, causing only 4 cycles of the first and second place cell firing to occur, in their proper order. (On occasion, some temporary convergence may occur as a place cell firing diminishes due to slow-AHP, although this was not the case for the first and second place cell firing here.) The PFC output was then connected to the same synaptic population on ECIII as the STM-buffer output.
Retrieval versus Exploration: In future experiments, the removal of the goal should cause the virtual rat to initiate exploratory behaviour, instead of continuing to recall learned episodes. This is implemented through circuitry that links both network output and random spikes that direct the virtual rat to a place field into the Feature De-Discretizer (the reverse I/O through the FeatureDiscretizer). The random events are suppressed by goal activity. This is done by feeding the output of PFC into an interneuron labelled "exploration-inhibition", via a strong synapse. That interneuron drives a strong GABA-ergic input with rapid rise time ($\tau_{rise}=0.1$ ms) and slow fall time ($\tau_{fall}=100$ ms and duration=125 ms) to a population of neurons that receive the random spiking events.
Necessary Operational Improvements: The following list of improvements is deemed necessary, after a review of the network performance, as depicted in graphs on the Ratlab Model Images page.
Smaller Place Fields: These may remove some of the difficulties involved with the turning of the corner stem-left and stem-right, and may remove difficulties associated with differing durations of the rat's presence in a place field. Keep in mind though, that smaller place fields will require either an even slower movement of the virtual rat, a larger memory buffer, a higher theta frequency or autoassociation of several small place cells into one episodic event. The FeatureDiscretizer output may also need to be more frequent, or the afferent conductances to the STM-buffer stronger.
The model prior to the following adjustments is saved as newtmaze.safe.ccm.
The first step is to increase the separation between the occurrence of consecutive place cell activities. I would like the traversal of one place field to span many theta cycles, yet at the same time I want to prepare the model for smaller place fields, which is a conflicting requirement. It almost looks as if the real culprit for this model implementation is the relatively long duration of the theta period. I am adjusting the trajectory parameters from pause=10 ms and speed=1 mm/ms to pause=1 ms and speed=0.15 mm/ms. This assures that each place cell will be active over at least 4 theta cycles, so that the total repetitions in STM due to slow AHP can be set to 7 theta cycles. The overlap with the next cell's firing in STM can be set to 3 theta cycles without causing three or more cells to spike within one theta cycle (since the STM buffer can currently reliably handle only 2 items). It seems to be difficult to avoid multiple afferent spiking without introducing a draconian fast AHP. Perhaps the frequency of the FeatureDiscretizer should be lowered, or the STM buffer should receive its input from the ECII input population. It would be useful if the ECII input population could be constructed to produce a single spike per item to be presented, regardless of the number of place cell spikes that occur. Temporarily, this is done in a very implausible manner, by giving ECII input cells a huge AHP. The conductance from the place input to the ECII input population also had to be increased to $G=0.16$ nS, so that spiking did not disappear due to dependence on ECIII. This is an interesting conundrum, since ECIII is supposed to influence this, but ECIII is now driven indirectly by ECII. Using afferent input from the ECII input population seems to work well, with an ADP with rise time $\tau_{rise}=400$ and conductance $G=5$ nS.
To avoid the misuse of the ECII input population, a separate STM input population is added. This population receives theta modulation of membrane potential, an input conductance of $G=3$ nS and strong AHP. A transmission modulation in synchrony with the membrane potential modulation was be added for extra precision. This population produces a single spike for each place field traversal, in sharp synchrony with theta oscillations. Either a phase difference in the theta oscillations, or a delay in the tranmission can be used to assure that the spikes arrive at the STM buffer in the encoding phase. Since extreem transmission delays may be implausible, I chose to change the phase of the STM buffer theta, as well as the STM buffer transmission modulation. Both were shifted by 100 ms (a phase difference of approximately -70 degrees). With this explicit phase alignment of afferent input, it is possible to modify the transmission modulation function to have the same GABA-ergic shape as the theta membrane potential modulation function, instead of the inverted form that was used to create a thinner transmission band.
Reverse-order STM buffer: An interesting discovery is the implementation of a reverse-order STM buffer. This can be achieved with an ADP with $\tau_{rise}=400$ ms, $\tau_{fall}=1$ ms, duration=180 ms, conductance $G=2.8$ nS and $E=-10$ mV. The ADP is then sufficiently gradual, that an afferent spike input is not repeated during the retrieval phase of the same theta period. In the subsequent theta cycle, the ADP of the new input will seem to have begun earlier than the ADP on other cells, causing it to spike in the first gamma cycle of the retrieval phase.
I have now made the ADP in the STM buffer so powerful ($\tau_{rise}=200 ms, $\tau_{fall}=1$ ms, $G=3$ nS) that a cell is certain to spike in the retrieval phase of the theta cycle in which it received afferent input. (Parameters $\tau_{rise}=400$ ms, $\tau_{fall}=1$ ms, $G=6$ nS would also achieve the certain spiking, but would require a medium AHP to avoid a cell that spikes at the very beginning of the retrieval phase from spiking again at the very end of the retrieval phase.)
2 verus 4 item STM buffer: Currently, the appearance of a third item, causes items 1 and 2 in the STM buffer to merge. The reason is that the afferent input of the third item causes a GABA-ergic gamma cycle that delays the spiking of the first item in the retrieval phase sufficiently that it slides into the same gamma cycle as the second item. This is not a problem at present, since we only want two items to be held. By setting the STM-buffer ADP parameters as above, but with $\tau_{rise}=300$ ms, the slope of ADP was decreased enough to maintain separation with 3 items in the STM-buffer (newtmaze.STM-3-items-20020130.ccm). The slippage at the presentation of the third item was prevented by adding transmission modulation (in synchrony with membrane potential modulation) to the recurrent GABA-ergic synapses responsible for gamma cycles.
Now the good STM-buffer behaviour must be retained while reactivating the slow AHP - or replacing it with a more specific means of deactivating older memory items - so that the desired two-item overlap sequences can be achieved for propagation to ECIII. (Optimally, but not necessarily biologically plausibly, we would like a function that allows STM retention to remain at full strength for 10 theta cycles, and thereafter shuts off the cell within one theta cycle.) A slow AHP with parameters $\tau_{rise}=1000$ ms, $\tau_{fall}=400$ ms, $G=0.25$ nS and duration=1200 ms seems to work. While it works for the first three place cells, it is obvious that the differing traversal durations can become problematic. There is only one occasion of proximity between PC3 and PC4 activity. A method by which a new item removes an old item from the buffer would be more reliable than one that depends on the timing of a specific slow AHP.
PC3 may also appear correctly, but it is somewhat difficult to be certain, since its activity is confused by the rapid return of the virtual rat whenever a stem-left or stem-right trajectory is taken. PC6 seems to appear in the correct phase when it does appear, but is probably skipped once (due to insufficient afferent activity), as noted above.
PC3 is retrieved in the correct phase, but does not manage to spike on the first theta cycle after its afferent presentation. PC4 has much the same issues as PC3. PC6 does not appear to be retrieved, or does not appear to be retrieved in the correct phase. Again, it seems to be suffering from insufficient presentation.
Operational Issues 20020131:
An optimal STM buffer for human memory acquisition has the following properties:
This should be achievable if the ADP can be made to drop off rapidly after a specific amount of time, although the cell's own capacitance will limit that rapidity. It is not desirable to fiddle much with the shape of the ADP as it currently is, since its relative steepness is very useful for reliably distinct STM spikes. If the buffer is full, the first item will be relatively close to the afferent input. The afferent input can cause something like a gamma cycle to delay the first item. The time between the spiking of the first item in successive theta cycles was already stabilized to about a theta period, so that an additional delay could bring it beyond the effective range of the ADP. This approach relies on several potentially implausible or difficult components to add: (i) rapid drop off of ADP after a duration equal to a theta period, (ii) an inhibition caused by the afferent spike that does not undo the reliability achieved by adding transmission modulation to the recurrent GABA-ergic input.
Perhaps the ADP rise time can be shortened further if the conductance is increased, thereby increasing the STM buffer capacity further, without losing robustness. The ADP can be stopped by setting the duration to about 130 ms. That may seem unrealistic, but really just involves the production of a different response function (not a double-exponential shape). That could be possible if a different intrinsic process begins to operate after the rise time of the ADP. When relying on gamma cycles to cause the suppression that would lead to the dropping of the first item, the parameter selection is extremely difficult and fragile. This does not look like a plausibly robust implementation.
I'm putting in a temporary cludge that is not biologically plausible, but will allow me to mull over the STM issue, while fixing the rest of the network! The previous version of the model, with slow AHP is retained in the copy newtmaze.STM-slowAHP.ccm.
Two other possibilities that may offer more plausible ways to replace STM items are:
The slow AHP, now responsible only for gradual deactivation without replacement by new items that is also caused by decoherence through noise, is set to $\tau_{rise}=3000$ ms, $\tau_{fall}=400$ ms, duration=4000 ms and conductance $G=0.05$ nS. These values can be easily modified if a retention greater than three seconds is necessary.
An interesting fact is that a slight increase of the ADP steepness ($\tau_{rise}=290$ ms) to insure that the spiking of the third item is not omitted just prior to the introduction of the fourth item, causes the fourth item to replace the first on its second theta cycle, but also causes it to take its place, out of order.
The main problem with all counter or integrator methods that deactivate the first item is that the new item cannot spike in the right order, because items 2 and on are still in their original slots within the theta period. For this reason, it might be better that whichever method is chosen should commence inhibiting as soon as the 3rd item enters the STM buffer. The inhibition can then be gradual, such as a slow AHP. The first item can then be deactivated a few theta cycles before the next afferent item appears, allowing all items to move into their new positions before the new item appears.
A third synapse population is added to the STM-shutoff cell population, which provides an offset that brings only cells that are spiking in the STM buffer closer to the threshold. With the parameters in the models newtmaze.inhibition-at-4th-item.ccm and newtmaze.inhibition-at-3rd-item.ccm, the first item is shut off at 4th and 3rd item presentations respectively. While neither model includes gradual shut-off, shut-off at the 3rd item presentation demonstrates that the method works when there is sufficient space for the new item to be retrieved in the same theta period. Obviously, a more plausible implementation of the method, that enables 3 item STM must eventually replace the current implementation. The power of the ADP needed to be increased ever so slightly ($\tau_{rise}=285$ ms and $G=3.2$ nS) for the 2 item STM version with shut-off at the 3rd item presentation, so that each new item would be retrieved within the theta period in which it was presented. This adjustment may not be necessary or desirable in other versions and future better implementations.
Problems of retrieval and encoding in the same theta periods:
If cells PC1 and PC2 spike in consecutive gamma cycles of STM and their activity is strongly transferred to ECIII, the LTP window will allow the synaptic strength from PC1 to P2 to be increased.
The goal activity from PFC needs to be synchronized with theta somewhat better, so about the same precision as that achieved by the input population that supplies afferent input to the STM buffer. There are two implementation options:
Note on Signal Timing Filters:
If the synchronized goal input and place input arrive within 10 ms of each other where they co-occur, the postsynaptic response at the PFC STM buffer must be slow enough to bridge that gap. A very small different in the synaptic delay on the two pathways to the PFC STM buffer mighty also be used for further synchronization if deemed plausible. Here, a slight difference in the timing of theta modulation in the two synchronizing filters is applied, so that the goal input and place input spikes occur only 3 ms apart. Because of this, it is possible to keep most of the parameters in the PFC STM buffer as they are in the EC STM buffer. The afferent input conductance in the PFC STM buffer is set to $G=9$ nS.
I have temporarily inactivated the slow AHP on the PFC STM buffer, since we are still using maintained firing in PFC to retrieve the goal location. A better implementation would store the goal information in LTP memory and retrieve it when the environment is entered.
Phases have been adjusted so that the PFC output arrives in the retrieval phase of ECIII. Theta modulation and transmission modulation (at afferent inputs and gamma input) in the PFC STM buffer is delayed by 164 ms (180 degrees out of phase with that of the EC STM buffer). Theta modulation of the synchronization populations on the input pathways to the PFC STM buffer is correspondingly delayed (56 ms on the goal input pathway and 62 ms on the place input pathway). The transmission modulation at those populations is also delayed by 62 ms.
The afferent goal information may have to arrive slightly later, as some interference with encoding activity still seems to develop. This can be tested by shifting the arrival times somewhat with synaptic delays. In addition to timing, the maximum efficacies afforded on recurrent fibres can insure that no retrieval is done outside of the retrieval phase. It works fairly well with maximum efficacy of $G=3.5$ nS and an afferent synaptic delay of 10 ms (with corresponding transmission modulation offset 97 ms). The balance of conductances in ECIII is further established with an afferent conductance from the EC STM buffer of $G=38$ nS (so that propagated spiking can occur in the encoding phase) and an afferent conductance from the PFC STM buffer of $G=23$ nS. Popagated spikes from the PFC STM buffer should then cause cue spikes only during the strongest portion of the retrieval phase, yet this is not always achieved, since ADP can aid spikes later in the retrieval phase. The effect of consequent undesired temporary event orders on synaptic efficacies may be controlled by adding LTD to the learning function.
The behaviour may be achieved by forcing retrieval and propagated spiking to coincide or by carefully separating encoding and retrieval phases, as described above. In either case, proper gamma cycles can be maintained, if desired, through a combination of slow NMDA channel responses, separation due to GABA-ergic gamma cycles, and a suppression of rapid double spikes by AHP. These dynamics must be incorporated in both the CA3 and ECIII layers. This should also work if the learning rate of LTP is not so steep as to cause saturated synaptic efficacies immediately. A gradually increasing level of activity in recurrent fibres from PC1 to PC2 should also be made to coincide with the activity imposed by propagation from the STM buffer.
It may also be helpful if episodic sequence recall depends on a cue that is longer than one item, Such a dependency can be arranged if the NMDA channel synapses saturate at efficacies low enough to require input from multiple items with slow responses. This may not be immediately implementable, as it requires a different context cue (multiple items) to begin episodic sequence retrieval for the goal-seeking recall behaviour. It may also require the use of a three item STM buffer during learning (which can be implemented by modifying the shut-off behaviour of the current STM buffer).
Shifting the plasticity modulation by 15 ms avoided learning between the first occurrance of the goal activity in ECIII and the first spike in a subsequent encoding phase.
Just before t=5000 ms, place cell 4 activates for the return trip along the left arm of the T-maze. The first spike of PC4 is only 20 ms before the retrieval spike of the goal location. That interval is within the LTP window, and the plasticity modulation at the goal retrieval spike is at a ratio of about 0.2 at that time. The synaptic efficacy is strengthened slightly (visible after t=5200 ms). This is not problematic in this particular case, since the pair PC5-PC4 should be encoded during the encoding phase at this stage anyhow. But it could be problematic if the same thing happens when PC3, PC2 and PC1 activate on the return trip. The optimal way to resolve this would assure that the appearance of place cell activity intended for the encoding phase does not occur within an interval to the first retrieval spike that is smaller than or equal to the LTP window or such that the plasticity modulation nullifies the LTP effect. This is necessary, since it is desirable that the LTP learning rate should be fairly great, so that pairs are encoded with the need for few repetitions. The LTP window also needs to be broad enough to capture all pairs. It is not a major difficulty, since these occurrances are fairly infrequent, unlike the many repetitions of retrieval spikes that can make even small ratios of the plasticity modulation add up significantly. The requirements are listed in Table 1. Since we do not wish to start retrieval later in the theta phase (there must be sufficient time to retrieve the path in ECIII) and we do not wish to make the LTP window narrower (all encoding pairs must be learned), there are three modifications that may be applicable: (1) the transmission modulation of encoding cells from the STM buffer can be made narrower, (2) the plasticity modulation of encoding cells can be made narrower, (3) STM gamma periods can be made narrower.
| functional phase | requirement |
|---|---|
| retrieval | At high theta modulation, the transmission modulation ratio and maximum efficacy on recurrent fibres should combine such that the items in a path are retrieved. |
| retrieval | At high theta modulation, the transmission modulation ratio and maximum efficacy on recurrent fibres should combine such that episodic retrieval ends early enough, so that the last retrieval spike is separated from the 2nd spike in the following encoding phase by an interval greater than the LTP window. |
| encoding | The 2nd spike in an encoding pair must fall within the high portion of plasticity modulation, and it must be separated from the 1st encoding spike by an interval less than the LTP window. |
| encoding | The 1st spike in an encoding pair should fall within the low portion of the plasticity modulation to avoid association with preceding retrieval spikes. |
| encoding | (a) The last spike in the encoding phase should be separated from the 1st spike in the retrieval phase by an interval greater than the LTP window, OR (b) the 1st spike in the retrieval phase should fall within the very low portion of the plasticity modulation. |
| encoding | The first onset of the 2nd encoding spike must be during the very low portion of the transmission modulation of recurrent fibre synapses to avoid recurrent retrieval of items in response to that encoding spike. |
Even if some of the details in the learning process may not be perfect yet, it does appear that the ECIII backwards spread turns out to work correctly after the full progression through the training trajectories. Near t=15000 ms, activity spreads in the expected sequence from the goal location to all other place cells. This state of the model is preserved in the version newtmaze.ECIII-spreading-backwards.ccm (20020212).
The backward path was not learned immediately on the first traversal down the stem, while the portions on the left arm were. This is indicative of the effect of the transmission modulation function, which affects the arm spikes less than the stem spikes, which must therefore be learned to a greater efficacy. An increased learning rate, or a more rapid recall may make the stem recall learnable in a single pass. The interval between recall spikes is about 8 ms at present. I am increasing the learning rate to 100, rather than the maximum synaptic efficacy in order to discourage retrieval in the absence of high theta. The synaptic efficacies between cells representing the stem of the T-maze are now sufficiently strong after a single pass, and the entire sequence is retrieved once the virtual rat has returned to its initial location. The synaptic efficacy from the EC STM buffer may need to be reduced slightly, since new second encoding spikes appeared after t=6000 ms and after t=9200 ms at offsets that are uncomfortably close to the first retrieval spike. I reduced the synaptic efficacy from $G=38$ nS to $G=30$ nS. The same modification is made in CA3. The appearance of new encoding spikes is now not as close to the retrieval phase, achieving a better separation through the transmission modulation. As noted above, this is not a major concern.
The learning rate on recurrent fibres may be increased if necessary. The maximum synaptic efficacy on recurrent fibres may be increased further to accommodate the retrieval of longer episodes. The synaptic delay on recurrent fibres in both ECIII and CA3 should probably be kept plausibly low (around 1-2 ms), while the rapid recall in ECIII (which may well be autoassociative in a forward-only implementation) and slower recall in CA3 (which may actually be achieved mainly through gamma input) can be expressed through synaptic response characteristics. A version of the model prior to these modifications was saved as newtmaze.20020214.ccm.
What is the current effect of the gamma input in ECIII? It would seem to make sense to have gamma input if the EC STM functionality and ECIII LTP functionality were integrated into a single population. In that case it would be useful to modulate the transmission on recurrent inhibitory fibres, so that inhibition would be minimal during the retrieval phase in ECIII, while it might be significant in CA3. I assume that the recurrent GABAergic inhibition will be useful, so I have temporarily ameliorated its effect on ECIII retrieval through transmission modulation in phase with the transmission modulation on synapses carrying encoding spikes from the EC STM buffer population.
Undesired autoassociativity: The backwards spread hypothesis relies on different activation times of place cells in ECIII, so retrieval must be sequential, not autoassociative. Currently, retrieval becomes autoassociative well above t=10000 ms, with a relatively large gap between goal activity and the autoassociative retrieval. I am investigating the cause of this. (The model that produces the responses discussed in this investigation is saved as newtmaze.20020213.ccm.) Between t=9600 ms and t=9900 ms, retrieval is still sequential, while spikes are being added for the right arm of the T-maze. Six items are recalled in the retrieval phase, including the goal location. Intervals differ quite a bit. Perhaps it is here, where small gamma periods should be included, if setting the synaptic response characteristics does not regulate recall sufficiently. It would be very useful to look at the actual efficacies as they develop. If it turns out that the very small ratio imposed by plasticity modulation still causes retrieved spikes to acquire significant mutual synaptic efficacies, either the plasticity modulation must be made narrower, or and LTD function may help. A display of the synaptic efficacies confirmed that LTP is gradually induced during retrieval phases, most rapidly on connections with the PC representing the goal.
After t=10250 ms, seven items are retrieved. The last item is a bit of a straggler, as the relatively slow influx of current (channel parameters are still set to $\tau_{rise]=2$ ms, $\tau_{fall}=4$ ms) needs more time to reach threshold at the prevailing ratio of transmission modulation in that phase. Strangely, the recall of item 6 was also quite removed from the goal activity, eventhough there are only 2 place fields between its place field and the goal place field, and strong efficacies should exist between the place cell representing the top of the stem and PC6. After t=11350 ms, many items are being retrieved much closer together, apparently approaching autoassociativity. After t=12350 ms, the retrieved items are bunched sufficiently that they begin to lose their proper order. The goal retrieval is consistently 5 ms prior to the onset of synaptic responses that recall the other items. Such intervals no longer exist between the items, suggesting, that synaptic efficacies exist between the goal PC and all other PCs that manage to recall them. For this to happen, an undesirable level of LTP learning must be occurring during retrieval phases.
One problem with these measures is that they contradict the desire to extend the duration of gamma cycles for robustness. Another is that they contradict the desire to use cues of more than one item to more reliably retrieve specific episodes, since such multi-item cueing implies significant synaptic efficacies between place cells in an episode that activate more than one step apart in the episodic sequence.
It may instead be possible to maintain large gamma cycle durations, by immediately implementing theta-cycle bridging for the recall of episodes longer than three items. The LTP-window, while relatively wide to accommodate the large gamma cycles, can then reliably affect only immediately adjacent items. If this is done and fewer retrieval spikes need to occur in a retrieval phase, then the goal-retrieval spike may occur later in the high portion of theta membrane modulation, thereby further separating encoding and retrieval spikes.
(20020215) The two implementational tasks that are best to concentrate on are:
|
Fixing the current implementation of ECIII learning for the current experiment:
One example of an attempt to use some of the suggestions above to tweak the model so that autoassociativity could be kept in check for the current experiment is saved in newtmaze.20020215-tweaked.ccm.gz. In it, the interneuronal population at ECIII ans the LTP function were replaced, the onset of goal retrieval was shifted (both the afferent activity and the transmission modulation), the excitatory and inhibitory recurrent synaptic parameters were modified. A better solution may be obtainable with shorter STM gamma cycles (perhaps doable by making the interneuronal population at the EC STM buffer react at a higher rate) and a correspondingly smaller LTP window, while gamma cycles keep retrieval spikes separated. The idea would be to make the interval between spikes in encoding and retrieval phases the same, while LTP can only affect adjacent spikes. This may not be quite plausible, given the empirical measurements for gamma cycles, and is investigated in the following paragraphs.
Further analysis of the cumulative autoassociativity problem: Could the durations of gamma cycles, theta cycles and the effect of LTP be plausibly chosen such that only ordered pairs of items become associated during residual plasticity in the retrieval phase? This scheme is depicted in the following figure.
The scheme may not be plausible, due to the probable typical durations of gamma and theta cycles and the relatively extensive presence of LTP effects. This problem is indicated in magenta in the figure above.
Reliable statements about plausible parameter values should be based only on (direct) measurements of the actual phenomena (oscillations in this case), not on hypotheses concerning their function. Examples of such measurements lead to the ranges in the following table.
| Theta | Gamma | ||
|---|---|---|---|
| S. Raghovachari | 4-10 Hz | J. Jefferys | 20-100 Hz |
| C.M. Krauses | 4-8 Hz | Lisman & Jensen | 20-60 Hz |
| M.J. Kahana | 4-8 Hz | S.C. Rowat | 25-100 Hz |
| M.E. Hasselmo | 30-80 Hz | ||
| abs. min-max | 4-10 Hz | abs. min-max | 20-100 Hz |
| av. min-max | 4-8.67 Hz | av. min-max | 24-85 Hz |
| conserv. min-max | 4-8 Hz =250-125 ms | conserv. min-max | 30-60 Hz =33.3-16.7 ms |
| average | 6 Hz | average | 45 Hz |
Worst and best case matching of theta and gamma periods from the conservative min-max ranges in the table above would allow between 3.75 and 15 gamma cycles to fit into a theta cycle. If we assume that theta and gamma cycle lengths covary, that longer theta cycles lead to longer gamma cycles, the fit is 7.5 gamma cycles per theta cycle at each extreme of the conservative ranges, which is then also the fit computed with the averages (6 Hz and 45 Hz). With such a fit, the hypothesis that encoding and retrieval phases occur in a theta cycle can for instance allow 3 spikes to occur in each phase (or 2 in the encoding phase and more in the retrieval phase) with some additional space to separate the two phases.
As stated in JEN:STMLTM1, the deactivation time coefficient for fast NMDA channels with NMDAR1a and NMDAR2a is about 36 ms, and that for slow NMDA channels with NMDAR1a and NMDAR2b/c about 300 ms. As long as the NMDA channel is not deactivated, postsynaptic activity can elicit some LTP. That LTP may accumulate over multiple repetitions, as when retrieval is repeated in many theta cycles. With these physiological timing coefficients, it is unlikely that no LTP effect will span a period greater than two gamma intervals (16.7 ms for 7.5 intervals in a 125 ms theta period, as implemented in the current model).
(At the slow extreme of the range of possible theta and gamma cycle durations, an LTP window that produces some effect over intervals greater than 30 ms may fit into the scheme above. If a theta period is 250 ms, a corresponding gamma cycle may have a period of 33.3 ms, so that two intervals (66.7 ms) may indeed exceed the persistence of an LTP effect.)
In a model implemented according to a forward-only hypothesis with episodic retrieval that loops through the system, a combination of factors may be able to stabilize retrieval: the shifting of groups of 3 items in each retrieval phase, a more plausible LTP curve that rewards shorter intervals between pre- and postsynaptic spiking more than longer intervals, a normalization achieved with LTD, and some residual plasticity modulation during retrieval phases.
A temporary fix (!) can be applied in an attempt to make the model work for the present experiment prior to any major redesign. For this, the already somewhat implausible plasticity modulation function can be made somewhat more implausible. It is currently implausible, since the function modulates plasticity between the extreem ratios of 0.0 and 1.0, while it is dubious if changes within a theta cycle can make synaptic efficacies entirely immutable. The temporary fix would assure that there is (a) a sufficiently long retrieval phase to retrieve all the items in a path and (b) a perfectly zero plasiticty modulation during that phase.
Application of this temporary fix produced the desired behaviour, with regular retrieval cycles for all items in a path (20020220). The items in the path to the right arm were retrieved in parallel, so that the first place cell on the right arm was retrieved, following the activation of the place cell at the top of the T. (Images of the activity produced by the model on 20020220 depict the stabilized behaviour.)
Multi-item cues:
Example (a) in the figure shows that not all place cells in episodes that include the current location are primed, since a more unique selection is made with the knowledge of the previous item. In this case, the backwards-spread can provide little additional information, as the multi-item cue may suffice to make a unique selection for subsequent episodic recall. Example (b) shows that backwards-spread can add useful information when the multi-item cue primes more than one overlapping episodic memory.
Problems: How might backwards-spread take place in non-spatial tasks? How can this hypothesis, together with multi-item cues use short-cuts (an issue highlighted by Example (a) in the figure above)?
Problems: How can this hypothesis, together with multi-item cues use short-cuts? Also, if the goal-context is bound to all items in episodes that lead to the goal, how would multi-item cues be an advantage for episode selection?
Eventhough the binding of goal-context with episodes may already resolve Example (b), it is important to remember that navigation is probably not based on euclidean space and a fixed resolution for PF sizes. Only the intended direction is needed as an output signal. This means that the entire ``stem'' of the T-maze can be represented as a single concept (item), a representation that can be achieved by an autoassociative item that does not depend on a large collection of specific features for reconstruction. The item can be cued by inputs provided by many overlapping feature percepts. In this context, such preprocessing/encoding can avoid having to handle many vastly overlapping episodic memories whose items individually have a very low information content.
It is not clear that the Lisman-Jensen approach to multi-item cued episodic recall is plausible, and yet:
As the context selects an episode to recall, on a forward-only basis, the problem in Example (b) of the figure above can be resolved uniquely, since the goal-context can have autoassociative subthreshold binding with the left [n] place cell.
These task-related selection mechanisms may exist at a higher cognitive level than the recall mechanisms used to produce the selected episodic memory.
The timing of afferent retrieval spikes from the ECII input population does not seem to be properly adjusted to the theta phase of CA3, but that phase should probably be adjusted to reflect the empirical phase difference between ECIII and CA3 (although this may instead be a matter of phase difference between the ECII STm buffer and CA3), and to aid the activity in CA1 elicited by the combination of ECIII and CA3 inputs.
A neuronal circuitry rule: There are two reasons to have multiple input sources to a population.
Driving CA1, current and alternative hypotheses:
Possible implementations of the backwards spread hypothesis are:
The alternative implementation 2 needs:
Point (i) in the figure of the current hypothesis for the backwards spread implementation indicates that ECIII must retrieve place cell 2 and place cell 1 prior to CA3 activation. That retrieval must propagate to CA1 so gradually that it can combine with the result of retrieval of place cell 1 and place cell 2 in CA3. This may argue against this implementation (and alternative implementation 1) of the backwards spread hypothesis. The alternative implementation 2 does not have this problem.
Point (ii) may also be more easily taken care of or avoided all-together in a forward-only hypothesis (a).
An additional preference for the chosen implementation is that it should work when bridging theta cycles or using higher levels of chunking to extend the length of a path beyond the number of items that can be rapidly recalled in ECIII during the retrieval phase. It would also be beneficial if the implementation could be used to some extent with a forward-only hypothesis