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Conceived and designed the experiments: JG TT SJE. Performed the experiments: JG. Analyzed the data: JG TT SJE. Contributed reagents/materials/analysis tools: JG SJE. Wrote the paper: JG TT SJE.

The authors have declared that no competing interests exist.

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.

Many central targets in the brain are involved in the processing of information from the outside world. Before information about the visual scene reaches the visual cortex, it is preprocessed in the retina and the lateral geniculate nucleus. Connections which relay this information between the different brain targets are not determined at birth, but undergo a developmental period during which they are guided by molecular cues to the correct locations, and refined by activity to the appropriate numbers and strengths. Before the onset of vision, spontaneous activity generated within the retina plays an important role in the remodeling of these connections. In a computational and theoretical model, we used recorded spontaneous retinal activity patterns with several plasticity rules at the retinogeniculate synapse to identify the key properties underlying the selective refinement of connections. Our model shows robust behavior when applied to both mouse and ferret data, demonstrating that a common plasticity rule across species may underlie synaptic refinements in the visual system driven by spontaneous retinal activity.

During the development of the visual system, connections between neurons form and refine in a self-organized manner governed by various mechanisms. Initially, target neurons are contacted by multiple RGCs following gradients of molecular cues

One possible mechanism of coincidence detection of pre- and postsynaptic activity is that of spike-time-dependent plasticity (STDP): synaptic change is induced from pairing multiple pre- and postsynaptic spikes, firing within tens of milliseconds of each other

To compare spike- and burst-based mechanisms in the remodeling of synaptic connections in a realistic developmental scenario, we examine the segregation of ON and OFF RGCs (which respond to light increments and decrements, respectively) onto postsynaptic neurons in the LGN. Early in development, individual LGN neurons receive inputs from

Here, we report results from a modeling study of the properties of experimentally-proposed synaptic plasticity rules and modifications to these rules necessary to capture the segregation of ON and OFF retinal inputs to a postsynaptic LGN neuron driven by recorded RGC spike trains

In

(A, left) An LGN neuron receives feedforward weak synaptic input from neighboring ON (red) and OFF (blue) RGC inputs early in development. (A, right) Spontaneous retinal waves selectively refine RGC inputs, such that synaptic weights of one RGC type (ON) strengthen, while weights of the other RGC type (OFF) decay to 0, resulting in an ON-responsive LGN neuron. Sample P12 spike rasters in the middle demonstrate that ON cells fire shorter bursts of higher spike frequency, while OFF cells fire longer bursts of lower spike frequency,

(A) STDP modifies synaptic strength based on the timing,

Set | 1 | 2 | 3 | 4 | 5 | 6 | |

# ON cells | 3 | 6 | 3 | 5 | 4 | 3 | |

# OFF cells | 3 | 2 | 2 | 2 | 2 | 5 | |

(Hz) | 1.51 | 0.40 | 0.70 | 1.01 | 0.34 | 1.04 | |

(Hz^{2}) |
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(s) | |||||||

(s) | |||||||

(Hz) | 2.94 | 0.63 | 0.80 | 2.44 | 2.06 | 2.48 | |

(Hz^{2}) |
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(s) | |||||||

(s) | |||||||

(Hz^{2}) |
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(s) | |||||||

(s) |

First, we studied a standard pair-based STDP rule with additive synaptic change (

In

(A) STDP with spike integration time windows of 20 ms results in ON/OFF segregation only for two data sets out of six (data set 1 shown here; data set 2 not shown), assuming a depression-to-potentiation ratio,

Comparing results from the reduced linear Poisson model and the simulated integrate-and-fire model for the other data sets (data not shown), however, did not produce consistent results as for data set 1. To simultaneously demonstrate the difference in outcomes between the two models, and the absence of segregation across all data sets, we computed a segregation index (Equation 16,

(A) Segregation indices using Equation 16 for all data sets following the linear modeling approach with STDP using unbiased initial conditions of 4.0 for both ON and OFF weights. By design the theoretical model always results in segregation for large enough

Unlike the reduced linear model, segregation in simulations with the integrate-and-fire model is harder to achieve, since it requires a subset of all weights of one cell type to potentiate maximally, while all weights of the other cell type to depress. Only in data sets 1 (

We also explored an STDP rule with a longer temporal window for synaptic depression than for potentiation corresponding to experiments from somatosensory cortex,

In conclusion, our modeling showed that a temporally-asymmetric plasticity rule like STDP, integrating pre- and postsynaptic spikes over short timescales on the order of tens of milliseconds which ignore the correlation timescales between inputs of different cell type, failed to segregate these ON and OFF RGC inputs in a model of a developing LGN over a wide range of parameters and in the absence of synaptic competition. Under STDP, the growth of synaptic weights of one cell type did not prevent the growth of weights of the other cell type, because ON and OFF cells fire independently within the timescale of STDP. Therefore, tightly correlated groups of ON and OFF cells which effectively drive the postsynaptic neuron, required physiologically-unrealistic, carefully-tuned values of the depression-to-potentiation ratio,

It is likely that synaptic plasticity rules work together with homeostatic mechanisms during formation and refinement of developing circuits

Model | set 1 | set 2 | set 3 | set 4 | set 5 | set 6 |

OFF | OFF | OFF | OFF | OFF | OFF | |

OFF | OFF | — | OFF | OFF | OFF | |

ON | ON | ON | ON | ON | ON | |

OFF | ON | ON | ON | OFF | ON | |

OFF | ON | ON | OFF | OFF | — | |

OFF | OFF | ON | OFF | OFF | — | |

— | OFF | — | OFF | OFF | — |

In the nonlinear integrate-and-fire model where multiple ON and OFF inputs were used, implementation of homeostasis also rescued segregation for biologically-plausible values of

In summary, we showed that adding subtractive normalization to STDP resulted in ON/OFF segregation but the outcome was highly sensitive to the choice of parameters. For biologically-realistic depression-to-potentiation values of

A spike-based rule like STDP cannot explain ON/OFF segregation in the LGN without synaptic competition because tightly correlated retinal inputs of different cell type reliably drive postsynaptic activity within 5–10 ms. Even with subtractive normalization, the short timescales of STDP are ineffective at robustly driving ON/OFF segregation. Butts and Rokhsar

Vector fields and example trajectories in

These modeling studies demonstrate that a plasticity rule for segregation does not only have to integrate pre- and postsynaptic activity over timescales matching those of the input correlations, but that other constraints are also required. Since the firing of ON RGCs precedes that of OFF RGCs, any rule which integrates activity over the second-long correlation timescales, must do so without giving a naïve advantage to the cell which fires first. STDP, on the contrary, favors synaptic inputs that can serve as ‘earliest predictors’ of other spike events

Can a temporally-symmetric burst-based rule integrating pre- and postsynaptic bursts over second-long timescales guide ON/OFF segregation in the LGN? Such a rule, BTDP, was experimentally-proposed for the developing retinogeniculate system and tested in a model for eye-specific segregation using simulated retinal waves

(A) Segregation results using BTDP for data set 1, a representative spike train recording of data sets 1–3 which have similar peaks of the pairwise input correlation for ON/ON and OFF/OFF pairs. Drawing conventions and legend as in

In

Parameter | Notation | Value |

EPSP kernel |
10 | |

100 | ||

5 | ||

50 | ||

STDP/BTDP | 0.001 | |

Integrate-and-fire | 0.02 | |

0.2 | ||

−50 | ||

2 | ||

30 | ||

STDP/BTDP |
0.0005 | |

0.0001 | ||

Upper synaptic bound |
5 | |

10 | ||

20 | ||

STDP |
20 | |

10 | ||

500 | ||

20 | ||

60 | ||

500 | ||

BTDP |
500 |

The segregation outcome under the reduced linear model for data set 4, as a representative of data sets 4–6, is illustrated in

To summarize, we found that not only the second-long timescales of bursts integration are needed for segregation, but also the temporally-symmetric feature of BTDP. In particular, the negative and symmetric BTDP window at long temporal delays in firing, mutually inhibited the simultaneous growth of ON and OFF synaptic weights, thus providing the necessary synaptic competition without implementing additional homeostatic mechanisms, in contrast to STDP. In

The ratio of final (

(A) Temporal evolution of synaptic weights with

Kerschensteiner and Wong

We showed that BTDP can explain ON/OFF segregation in the developing LGN of mouse by integrating activity (i) over timescales relevant to the inputs, and (ii) irrespective of the order of pre- and postsynaptic activity. Furthermore, half of the studied data sets (1–3) demonstrated dominance of ON segregation, and the other half (sets 4–6) demonstrated dominance of OFF segregation. To understand why BTDP successfully captured segregation without additional homeostatic mechanisms (but not standard STDP, nor STDP with extended timescales), and to determine which features of the inputs specified ON versus OFF dominance, we dissected the linear model of Equation 7 (

For comparison, in STDP with subtractive normalization the RGC firing rates dominated segregation due to the millisecond-long integration timescales, while the contribution from the correlations cancelled due to the temporal asymmetry of STDP. In BTDP, however, we show that the RGC correlations dominate segregation due to the matching second-long integration timescales, and are further intensified by the temporal symmetry of BTDP. The entries in the plasticity matrix

(A) (left) ON dominance. Factors which determine segregation for data sets 1–3 (data set 1 in

A matrix of this form has eigenvalues

Even though this interpretation of the reduced linear model does not directly use the recorded spike trains in each data set (whereas the simulated integrate-and-fire model does), but instead uses fitted estimates of the correlations computed from the most correlated cell pairs, results from the linear and integrate-and-fire models agree (

In

Extending integration timescales of STDP to the relevant input correlation timescales results in the plasticity matrix

In summary, we have shown that BTDP can explain ON/OFF segregation in the developing mouse LGN driven by spontaneous retinal waves. BTDP promoted cooperation between weights of same type cells and competition between weights of different type cells without additional homeostatic control. We predicted that the LGN neuron will become ON- or OFF-responsive based on a local competition of the firing patterns of neighboring RGCs connecting to it, whose most relevant features for segregation are contained in the pairwise temporal correlations. As ON bursts are shorter than OFF bursts as suggested by the smaller correlation timescales, under BTDP this would suggest dominance of ON segregation. However, if OFF bursts are more highly correlated as suggested by the higher correlation peaks, then the result is dominance of OFF segregation. In particular, we saw that ON and OFF RGCs with sufficiently-different firing properties to compete for the wiring of the LGN neuron, are located close to each other (within 50

The BTDP model we just described suggests how spontaneous retinal waves can instruct ON/OFF segregation in individual LGN neurons in mouse. Is this result specific to mouse RGCs, or might this model explain segregation in other systems? The firing properties during retinal waves in ferret significantly differ from those in mouse

Using the recorded spike trains from the Lee at al. study (15 sets in

Earlier we showed that BTDP failed to induce ON/OFF segregation in mice when the one-second firing offset between the ON and OFF cells was eliminated. Although ON and OFF cells fire synchronously in ferret, BTDP could still induce segregation because the correlation between cells of different type in ferret falls off much slower than the correlation between cells of different type in mouse (

We have used analytical methods and computational simulations to test the hypothesis that spontaneous retinal activity guides the segregation of ON and OFF RGCs in the developing mouse LGN. We have compared two plasticity rules for the development of synaptic weights: STDP and BTDP. Modifications to these rules adapted to the characteristics of the input firing patterns have also been considered. Our results show that STDP alone fails to segregate ON and OFF inputs under realistic ratios of depression-to-potentiation. STDP can segregate mixed inputs when combined with a homeostatic mechanism such as subtractive normalization, however the results are highly sensitive to parameters. By comparison, the recently-proposed BTDP rule

Twenty years after the initial discovery of retinal waves, there is still an ongoing debate on if, and how, spontaneous activity influences the development of neural connections

In this paper we have taken two complementary approaches to studying segregation of ON and OFF inputs. With simulations, we were able to use the experimentally observed RGC spike trains to generate spiking behavior in a nonlinear integrate-and-fire model; by contrast with a reduced linear model we used only the input correlations of the most correlated cells. The broad similarity in our results between simulation and theory under the more relevant BTDP plasticity rule suggests that the mechanisms for synaptic change guided by spontaneous retinal waves are robust and do not require the precision of individual spikes. Thus, the effect of future manipulations of activity on segregation would not need to be tested with complex spiking models, but predictions can be made with simpler models which use spike-spike correlations over the relevant timescales. Detailed models of retinal wave activity could also help investigate this question, however currently they only model the early cholinergic waves

Unsurprisingly, we found that a synaptic plasticity rule like STDP, which integrates spikes on much shorter millisecond-long timescales than the relevant timescales of the input correlations, failed to segregate ON and OFF inputs. STDP usually resulted in the strengthening of synaptic weights of both cell types, suggesting a lack of competition. STDP induces competition among synaptic weights when the depression area of the STDP window is slightly larger than the potentiation area (

In addition to normalization constraints, it is possible that segregation might result from an alternative implementation of a spike-based plasticity rule which involves higher-order spike integration

We believe a burst-based rule is most relevant for retinogeniculate development for several reasons. It reflects the firing patterns of RGCs during spontaneous retinal waves; by contrast, STDP rules have been proposed for mature sensory systems where single spikes can evoke postsynaptic activity

In contrast to STDP with subtractive normalization, BTDP utilized the RGC correlations over the relevant second-long timescales to generate segregation without parameter sensitivity (for instance, to

Our model with BTDP also successfully explained ON/OFF segregation in ferret where ON and OFF RGCs fire synchronously, but with a higher firing rate for OFF RGCs than ON

In addition to segregation of RGCs onto individual LGN neurons, neighboring LGN neurons within a sublamina in ferret respond to the same cell type

Experiments which manipulate correlations between RGCs without eliminating spontaneous activity itself have proven extremely useful in answering the key question of whether retinal waves influence development. Recent work reports that mice lacking the

A synaptic weight representing the strength of the connection between the

Instead of using the full set of ON and OFF spike trains from each data set, we used pairwise spike-spike correlations as inputs, and simulated postsynaptic activity with a linear model, following the approach of Kempter et al.

Representing the output neuron with a linear Poisson model allows us to write a linear system for the weight dynamics

Instead of studying the evolution of all ON and OFF weights for each data set, we studied a reduced system with a two-dimensional weight vector

In the analysis of STDP, we observed a mismatch between the results from the reduced linear and the nonlinear integrate-and-fire models (

The retinal wave structure of the inputs manifests itself in LGN neurons as large periodic barrages of postsynaptic currents which drive bursts of action potentials

Unlike the linear model, here we studied the temporal evolution of ON and OFF weights for all inputs in each data set. To compare results with the reduced linear model where a single ON and a single OFF weight were studied, we assigned all ON weights the same initial strength, and all OFF weights the same initial strength (but different from the initial strength for ON). Testing different initial conditions for all 5–8 weights per data set would have required a representation of the weight dynamics in a 5–8-dimensional space. Choosing the same initial condition for all ON and for all OFF weights, we ran a separate simulation for each initial condition combination. Segregation of the inputs was interpreted as the depression of all weights of one cell type, and the maximal potentiation of some weights of the other cell type. As we simulated the dynamics in the full weight space with all available spike trains in each data set, a succinct two-dimensional representation as for the linear model was unfeasible. Note that all ON and OFF inputs in each data were used when that particular data set was explored; spike trains were not mixed between data sets. Total number of retinal afferents in each data set were 5–8 (

According to pair-based STDP, synaptic weights were modified based on pairings between pre- and postsynaptic spikes separated by

In contrast to STDP, BTDP is temporally-symmetric, such that the timing but not the order of the bursts determines the sign of synaptic change over second-long timescales

The function describing synaptic change according to BTDP was experimentally fitted by Butts et al.

For the derivation of the linear system with BTDP, we used the spike-spike input correlations as for STDP (statistics given in

To ensure smooth synaptic weight dynamics over time, we used relatively small values of maximum potentiation and depression amplitudes in each rule (

To quantify the degree of segregation, we used the following measure

Subtractive normalization was implemented at the level of individual neurons following findings in superior colliculus, where the number and the strength of retinal afferent synapses received by a postsynaptic neuron was preserved during development

A comparison between the model in Lee et al. (2002) and BTDP.

(0.06 MB PDF)

Segregation results for ferret using STDP and BTDP.

(0.03 MB PDF)

Correlation fits for ferret.

(0.03 MB PDF)

Spiking data from mouse and ferret.

(0.70 MB ZIP)

C code for implementing STDP and BTDP.

(0.07 MB ZIP)

Daniel Kerschensteiner and Rachel Wong kindly provided the mouse data; the ferret data came from Christopher Lee-Messer. Thanks to Jonathan Dawes and Jean-Pascal Pfister for helpful discussions, and Keith Godfrey for reading drafts of this paper.

^{2+}-mediated plateau potential in developing relay cells in the LGN.