Burst-Time-Dependent Plasticity Robustly Guides ON/OFF Segregation in the Lateral Geniculate Nucleus

Spontaneous retinal activity (known as “waves”) remodels synaptic connectivity to the lateral geniculate nucleus (LGN) during development. Analysis of retinal waves recorded with multielectrode arrays in mouse suggested that a cue for the segregation of functionally distinct (ON and OFF) retinal ganglion cells (RGCs) in the LGN may be a desynchronization in their firing, where ON cells precede OFF cells by one second. Using the recorded retinal waves as input, with two different modeling approaches we explore timing-based plasticity rules for the evolution of synaptic weights to identify key features underlying ON/OFF segregation. First, we analytically derive a linear model for the evolution of ON and OFF weights, to understand how synaptic plasticity rules extract input firing properties to guide segregation. Second, we simulate postsynaptic activity with a nonlinear integrate-and-fire model to compare findings with the linear model. We find that spike-time-dependent plasticity, which modifies synaptic weights based on millisecond-long timing and order of pre- and postsynaptic spikes, fails to segregate ON and OFF retinal inputs in the absence of normalization. Implementing homeostatic mechanisms results in segregation, but only with carefully-tuned parameters. Furthermore, extending spike integration timescales to match the second-long input correlation timescales always leads to ON segregation because ON cells fire before OFF cells. We show that burst-time-dependent plasticity can robustly guide ON/OFF segregation in the LGN without normalization, by integrating pre- and postsynaptic bursts irrespective of their firing order and over second-long timescales. We predict that an LGN neuron will become ON- or OFF-responsive based on a local competition of the firing patterns of neighboring RGCs connecting to it. Finally, we demonstrate consistency with ON/OFF segregation in ferret, despite differences in the firing properties of retinal waves. Our model suggests that diverse input statistics of retinal waves can be robustly interpreted by a burst-based rule, which underlies retinogeniculate plasticity across different species.

Substituting this into Equation 1 above, yields where C ij = x j x i is the raw input correlation matrix and x j is the average activity of x j .
To show how the form of Equation 4 compares to our linear system for ON/OFF segregation under BTDP, we let where x = (x 1 , x 2 ) T , n = (1, 1) T and T denotes the transpose. Then Equation 4 becomeṡ we can make a direct correspondence between the role of R in the plasticity matrix Q (Equation 1 Text S1 in Results and Figure   C ii > C ij and C ii > C ji (with C ij = C ji and i = j).
Therefore, subtracting the amount x i θ from row i in C gives positive terms on the main diagonal (due to the larger entries C ii ), and negative terms otherwise (due to the smaller off-diagonal entries C ij ). Thus, the main diagonal entries in Q * are positive and the off-diagonal entries are negative, i.e.
With this formulation, the off-diagonal terms in Q * of the Lee et al. [1] model are not equal as the terms x in Q of our linear model with BTDP (even though C ij = C ji , a different amount x j θ was subtracted from each C ij ). In this sense, our linear model of BTDP differs from the covariance-based model of Lee et al. [1]. As we discussed in Results, and in agreement with models of ocular dominance segregation, however, competition between the ON and OFF weights arises provided the off-diagonal entries in the plasticity matrix Q or Q * are negative [2]. Which cell wins the competition depends on the dominant term on the main diagonal in the plasticity matrix. Both of these conditions hold in our model with BTDP and in the Lee et al. [1] model. For the mouse data, we found a natural division among the sets (Table 1): some sets showed dominance of ON segregation (1-3), while others showed dominance of OFF segregation (4-6). For the ferret data, however, the segregation outcome was in favor of the more frequently-firing OFF cell (Table S1), consistent with the model in Lee et al. [1]. To allow for ON segregation (as LGN neurons are both ON-and OFF-responsive [3]), Lee at al. [1] introduced an inhibition term Γ which silenced the more-active (OFF) cell allowing the less-active (ON) cell to win.
The functional implications of this term are further discussed in [1].
This text demonstrates how different plasticity rules can be reduced to the same mechanism to explain ON/OFF segregation in two different species. We showed that a simple covariance-based Hebbian plasticity rule with an interaction term θ which can explain ON/OFF segregation in ferret, can be related to a realistic plasticity rule, BTDP, which successfully captures ON/OFF segregation in both mouse and ferret. This suggests that the rules which govern ON/OFF segregation may be shared between species.