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. 2014 Jun 1;111(11):2355-73.
doi: 10.1152/jn.00891.2013. Epub 2014 Mar 5.

Emerging Feed-Forward Inhibition Allows the Robust Formation of Direction Selectivity in the Developing Ferret Visual Cortex

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Free PMC article

Emerging Feed-Forward Inhibition Allows the Robust Formation of Direction Selectivity in the Developing Ferret Visual Cortex

Stephen D Van Hooser et al. J Neurophysiol. .
Free PMC article

Abstract

The computation of direction selectivity requires that a cell respond to joint spatial and temporal characteristics of the stimulus that cannot be separated into independent components. Direction selectivity in ferret visual cortex is not present at the time of eye opening but instead develops in the days and weeks following eye opening in a process that requires visual experience with moving stimuli. Classic Hebbian or spike timing-dependent modification of excitatory feed-forward synaptic inputs is unable to produce direction-selective cells from unselective or weakly directionally biased initial conditions because inputs eventually grow so strong that they can independently drive cortical neurons, violating the joint spatial-temporal activation requirement. Furthermore, without some form of synaptic competition, cells cannot develop direction selectivity in response to training with bidirectional stimulation, as cells in ferret visual cortex do. We show that imposing a maximum lateral geniculate nucleus (LGN)-to-cortex synaptic weight allows neurons to develop direction-selective responses that maintain the requirement for joint spatial and temporal activation. We demonstrate that a novel form of inhibitory plasticity, postsynaptic activity-dependent long-term potentiation of inhibition (POSD-LTPi), which operates in the developing cortex at the time of eye opening, can provide synaptic competition and enables robust development of direction-selective receptive fields with unidirectional or bidirectional stimulation. We propose a general model of the development of spatiotemporal receptive fields that consists of two phases: an experience-independent establishment of initial biases, followed by an experience-dependent amplification or modification of these biases via correlation-based plasticity of excitatory inputs that compete against gradually increasing feed-forward inhibition.

Keywords: Hebbian learning; Reichardt detector; feed-forward; logical AND-gate; unsupervised learning.

Figures

Fig. 1.
Fig. 1.
An excitatory feed-forward model of direction selectivity. A: a model circuit with 4 lateral geniculate nucleus (LGN) inputs in a 2 × 2 configuration; the LGN units in each row respond to different stimulus positions, while the units in each column respond to different stimulus latencies (1st column latency is 0, 2nd column latency is Δt). These units project to a cortical neuron V with the synaptic conductances indicated. B: while this paper posits that units with different latencies are in the LGN, if the cells with longer-latency responses reside in the cortex, then the behavior of the circuit is the same. C: a simulation with all synaptic weights equal to 75% of the amount necessary to produce an action potential in cortical cell V. The bar stimulus first moves upward and then downward. The bar first arrives at the lower stimulus position, which immediately activates unit u11. The bar next arrives at the upper stimulus position at time Δt; at that time, unit u12 responds to the stimulus at the lower position (because it has a latency of Δt) while unit u21 responds to the stimulus in its receptive field. The simultaneous activation of units u12 and u21 drives cortical cell V to fire action potentials. The process is reversed for downward motion. DSI, direction selective index; Vm, membrane potential. D: a selective model. Only units u12 and u21 have nonzero synaptic conductances; the cortical cell fires only for upward motion. E: synapses that are too strong cause reduced selectivity. The weights of u12 and u21 have been increased to 110% of threshold; the cortical neuron's selectivity is reduced, as activation of either u12 or u21 is sufficient to drive V; joint activation of u12 and u21 is no longer required. F: a model with a 5 × 5 LGN matrix, demonstrating that additional inputs allow increased firing rates of V with maintained selectivity. Conductances that are activated before the set of 5 LGN neurons that comprise the “upward diagonal” are indicated as Gearly, and those activated after are indicated as Glate.
Fig. 2.
Fig. 2.
Spiking responses in the developing ferret visual cortex. A: average cell responses to 20 cycles of drifting gratings presented at 4 Hz (that is, 20 bar presentations) for 3 groups of ferrets from Clemens et al. (2012). Animals marked “eyes closed” had closed eyelids at the beginning of the experiment; eyelids were opened by the experimenter. Animals marked “Eyes open, PND<35” had naturally open eyelids at the beginning of the experiment but were younger than postnatal day (PND)35; on average these animals had ∼2 days of visual experience. Animals marked “Eyes open, PND≥35” had their eyes open at the beginning of the experiment and were PND35 or older; these animals had 4 or more days of visual experience. B: responses per bar in the preferred (y-axis) and null (x-axis) directions for individual cells for the 3 groups. Compare to Fig. 3D. C: DSI vs. response in the null direction. Compare to Fig. 3F.
Fig. 3.
Fig. 3.
Capabilities of the excitatory feed-forward model. A–C: limitations of models with 2 × 2 LGN configurations. Red and green bars indicate the boundaries of combinations of Rpref and Rnull that can exist in a linear threshold (LT) simplification of the computational model. The maximum difference between Rpref and Rnull is constrained to be ≤ a constant (see text). Shaded area indicates region where model can operate. Dots indicate computational models with randomly generated synaptic conductances. Note that these dots largely fall within the predicted region; some models slightly exceed the bounds because the response of an integrate and fire (I+F) neuron to input is nonlinear (see text). Blue lines indicate maximum direction selectivity; direction selectivity is constrained to be less than or equal to the blue line (shaded region). C is a zoomed-in view of B. D–F: response combinations and direction selectivity possible for N × N LGN configurations, where N is the number indicated on each curve. D: red lines indicate maximum Rpref that is possible for each value of Rnull. Green line indicates the minimum value of Rpref as equal to Rnull. E and F: blue lines indicate maximum direction selectivity that is possible. F is a zoomed-in view of E. Compare to Fig. 2, B and C.
Fig. 4.
Fig. 4.
Unidirectional training in a 2 × 2 model. A: training with classic spike timing-dependent plasticity (STDP) where synaptic weights are allowed to grow large. The conductances that support the upward direction (G12, G21) increase with each presentation of the stimulus. During stimuli 6–8, the cortical cell exhibits moderate direction selectivity. However, as the weights continue to increase, activations of units u12 or u21 alone are sufficient to drive activity in cortical cell V and joint activation of u12 and u21 is no longer required. After stimulus 9, the responses to the downward direction increase and DSI falls back to 0. B: training with classic STDP but with an imposed ceiling of 6.64 nS on the maximum synaptic conductance. The cell exhibits moderate direction selectivity that is stable. Note that the smaller weight changes per trial and the larger amount of stimulation necessary to induce direction selectivity in B are a result of the classic STDP equation, which produces, after each pre-post spike pairing, a conductance increase that is in proportion to the maximum allowable conductance.
Fig. 5.
Fig. 5.
Constrained synaptic weights and STDP allow the development of direction selectivity during unidirectional motion training. A: results of simulations for circuits with a 5 × 5 LGN, Δt as indicated, and where the output cell initially responded unselectively, with 1 spike to each direction. Top: final DSI achieved. Bottom: responses in the preferred direction after training. B: the initial and final values of synaptic conductances from the 5 × 5 LGN with classic STDP and a latency step size of 0.25 s. The “early” LGN synaptic conductances that are activated before the “upward diagonal” are highlighted in yellow, while the “late” LGN synaptic conductances that are activated after the “upward diagonal” are highlighted in orange (see Fig. 1E). C: the early conductances exhibit increases with training, while the “late” synaptic conductances typically decrease as a result of training, particularly for short lags (Δt < 100 ms). Dashed blue lines indicate calculated Giceil, dashed red lines indicate initial Gi. D–F: same as A–C, for triplet STDP rule.
Fig. 6.
Fig. 6.
Constrained synaptic weights and classic STDP (A–D) and triplet STDP (E–H) do not permit the development of robust direction selectivity with bidirectional training. A: bidirectional training (upward followed by downward) in a cell that initially exhibited no directional bias. DSI has a sign; positive values indicate that the response in the upward direction is greatest, while negative values indicate that the response in the downward direction is greatest. The responses to both the upward and downward directions increase as a result of bidirectional training, but direction selectivity does not increase. B: bidirectional training in a cell that initially exhibits a suprathreshold directional bias for the upward direction. The response to the downward direction increases, while the response to the upward direction, which was already near its ceiling, decreases slightly. Direction selectivity weakens as a result of bidirectional training. C and D: summary of the impact of bidirectional training and unidirectional training with constrained synaptic weights and classic STDP. x-Axis indicates initial directional bias. Symbols S+2 and S+ indicate subthreshold directional biases in the upward direction, where initial conditions were set to those obtained with 27 and 55 upward directional sweeps such that the cortical cell fired 1 spike in each direction (shown in Fig. 4B); S−2 and S indicate subthreshold biases in favor of the downward direction, similarly defined. y-Axis indicates final DSI values obtained or change in DSI values from initial conditions. Bidirectional training cannot produce robust direction selectivity, although unidirectional training produces strong direction selectivity for the trained stimulus. E: for some initial conditions, such as S+2, bidirectional training with triplet STDP can produce full direction selectivity in the biased direction. F: other initial biases are not amplified by bidirectional training, and full direction selectivity is not achieved. G and H: summary of the impact of bidirectional training and unidirectional training with constrained synaptic weights and triplet STDP.
Fig. 7.
Fig. 7.
A feed-forward circuit with postsynaptic activity-dependent long-term potentiation of inhibition (POSD-LTPi). A: modification of the model in Fig. 1 to include feed-forward inhibition. LGN units provide input to a feed-forward inhibitory interneuron, which in turn provides inhibition to the cortical excitatory neuron that is monitored as the output of the circuit. B: POSD-LTPi is present around the time of eye opening and increases with burst activation of the postsynaptic excitatory cell; activation of the interneuron is irrelevant to the increase in inhibition (Garkun and Maffei 2014). We model this as a small increase in inhibition with each training stimulation. C and D: illustration of the impact of increasing spike threshold (equivalent to increasing broad inhibition) on the circuit. Circles labeled a–e denote the level of threshold, which increases from a to e. The firing rate combinations Rup and Rdown and the direction selectivity DSI that are achievable do not change; as before (Fig. 3), the circuit can only produce activity within the shaded reasons. However, starting from position a, increasing threshold brings the circuit into a region where it is capable of expressing a wide variety of DSI values. E: illustration of increasing inhibition (α to δ) on a direction tuning curve. Increasing inhibition causes increased selectivity and increased competition among the feed-forward excitatory synapses that support the 2 peaks.
Fig. 8.
Fig. 8.
Constrained synaptic weights, STDP, and POSD-LTPi allow the development of robust direction selectivity with bidirectional training, including amplification of initial directional biases. A: bidirectional training (upward followed by downward) in a cell that initially exhibited no directional bias. DSI has a sign; positive values indicate that the response in the upward direction is greatest, while negative values indicate that the response in the downward direction is greatest. The responses to both the upward and downward directions increase as a result of bidirectional training, but direction selectivity does not increase. B: bidirectional training in a cell that initially exhibits a subthreshold directional bias for the upward direction (conductances set to S+, defined below). The response to the downward direction decreases slightly, while the response to the upward direction increases. The cell acquires a strong preference for the upward direction. C: same as B, for a cell with a suprathreshold bias for the upward direction. D: unidirectional training with POSD-LTPi can cause a cell to acquire a strong direction preference that is opposite to its initial bias. Cell initially exhibits a suprathreshold bias for the downward direction, but unidirectional training with the upward direction produces strong final direction selectivity for the upward direction. E and F: summary of the impact of bidirectional training and unidirectional training with constrained synaptic weights, STDP, and POSD-LTPi. x-Axis indicates initial directional bias. Symbols S+2 and S+ indicate subthreshold directional biases in the upward direction, where initial conditions were set to those obtained with 27 and 55 upward unidirectional sweeps in classic STDP (1 spike in each direction as shown in Fig. 4B); S−2 and S indicate subthreshold biases in favor of the downward direction, similarly defined. y-Axis indicates final DSI values obtained or change in DSI values from initial conditions.
Fig. 9.
Fig. 9.
The model is robust over a moderate region of parameter space. Plot of final direction selectivity after 1,000 iterations of bidirectional training. For A and B, the model was started with an initial direction selectivity value of 0.5. A: classic STDP. B: triplet STDP. Color indicates the final DSI value achieved, according to the scale at right. The Giceil and Imax parameters were varied relative to the parameters used in Fig. 8 with the scale factors shown. The model acquires direction selectivity for a wide range of parameter values. The model is most sensitive to the value of Giceil. When no POSD-LTPi is used (Imax = 0), the model can tolerate a 12% variation of Giceil (red region in left column of each graph). When sufficient POSD-LTPi is present, the model can acquire strong direction selectivity over a range of Giceil >35% (red region, right columns). C and D: same as A and B, but for an initial direction selectivity of S+ (see Figs. 6 and 8). For classic STDP (C) the model was very sensitive to the parameters, achieving full direction selectivity over a narrow range of Giceil and POSD-LTPi, while the triplet model (D) was less sensitive for this subthreshold initial bias.
Fig. 10.
Fig. 10.
Illustration of the dynamics of changes in synaptic weights and direction selectivity in the feed-forward model for a 2 × 2 LGN. In the absence of POSD-LTPi the circuit remains in A and D, while inclusion of POST-LTPi causes the circuit, which initially follows A and D, to progress through the dynamics indicated in B and E and then C and F. A: under unidirectional training with upward motion without POSD-LTPi, the synaptic weights that support the response to upward motion (Wx) will increase, provided that the synaptic weights are sufficiently strong to permit a response to upward motion (right half of graph). For each pair of synaptic weights Wx and Wy, arrows indicate the changes in synaptic weights for a single iteration of the model. In this graph, all arrows point to right, indicating that Wx will increase at every position and Wy will not change. The false color image indicates the DSI value for each pair of synaptic weights Wx and Wy. The white circle indicates the position of an example starting condition and how it changes over time. Without POSD-LTPi, the ending condition is indicated by the gray square. With POSD-LPTi, the subsequent states are indicated by the white circles on subsequent panels. B: when POSD-LTPi is employed, inhibition increases with every stimulus bout. Increases in inhibition are weak at first, much like A, but then become larger, like B. The increased inhibition causes an effective increase in threshold T, and a corresponding effective decrease in both Wx and Wy, that is added to the effect of STDP, such that overall Wy is reduced and Wx is increased. C: as inhibition grows with POSD-LTPi, the change in inhibition for each stimulus bout increases and the effective synaptic weight of Wy is pushed strongly to 0 while Wx, which likely grew stronger during previous stimulus bouts, is increased further. When inhibition hits its ceiling, the dynamics return to that depicted in A, with the final stable state indicated by the black box. D: under bidirectional training without POSD-LTPi, synaptic weights Wx and Wy exhibit increases but DSI values are not altered. E: with POSD-LTPi, as inhibition grows slowly, any initial biases are selectively amplified such that direction selectivity for the initially biased direction increases (arrows point toward red and blue quadrants). F: as inhibition grows further with POSD-LTPi, initial biases are more strongly amplified. Under previous stimulation, the weights Wx or Wy would have increased strongly (depending upon the initial bias); with stronger increases in inhibition, the arrows point toward red and blue quadrants for larger Wx or Wy. When inhibition reaches the ceiling, the dynamics return to those in D, with the final stable state indicated by the black box.

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