Stability and Competition in Multi-spike Models of Spike-Timing Dependent Plasticity

Spike-timing dependent plasticity (STDP) is a widespread plasticity mechanism in the nervous system. The simplest description of STDP only takes into account pairs of pre- and postsynaptic spikes, with potentiation of the synapse when a presynaptic spike precedes a postsynaptic spike and depression otherwise. In light of experiments that explored a variety of spike patterns, the pair-based STDP model has been augmented to account for multiple pre- and postsynaptic spike interactions. As a result, a number of different “multi-spike” STDP models have been proposed based on different experimental observations. The behavior of these models at the population level is crucial for understanding mechanisms of learning and memory. The challenging balance between the stability of a population of synapses and their competitive modification is well studied for pair-based models, but it has not yet been fully analyzed for multi-spike models. Here, we address this issue through numerical simulations of an integrate-and-fire model neuron with excitatory synapses subject to STDP described by three different proposed multi-spike models. We also analytically calculate average synaptic changes and fluctuations about these averages. Our results indicate that the different multi-spike models behave quite differently at the population level. Although each model can produce synaptic competition in certain parameter regions, none of them induces synaptic competition with its originally fitted parameters. The dichotomy between synaptic stability and Hebbian competition, which is well characterized for pair-based STDP models, persists in multi-spike models. However, anti-Hebbian competition can coexist with synaptic stability in some models. We propose that the collective behavior of synaptic plasticity models at the population level should be used as an additional guideline in applying phenomenological models based on observations of single synapses

Pairwise Analysis Can Account for Network Structures Arising from Spike-Timing Dependent Plasticity

Spike timing-dependent plasticity (STDP) modifies synaptic strengths based on timing information available locally at each synapse. Despite this, it induces global structures within a recurrently connected network. We study such structures both through simulations and by analyzing the effects of STDP on pair-wise interactions of neurons. We show how conventional STDP acts as a loop-eliminating mechanism and organizes neurons into in- and out-hubs. Loop-elimination increases when depression dominates and turns into loop-generation when potentiation dominates. STDP with a shifted temporal window such that coincident spikes cause depression enhances recurrent connections and functions as a strict buffering mechanism that maintains a roughly constant average firing rate. STDP with the opposite temporal shift functions as a loop eliminator at low rates and as a potent loop generator at higher rates. In general, studying pairwise interactions of neurons provides important insights about the structures that STDP can produce in large networks

A neural circuit mechanism for regulating vocal variability during song learning in zebra finches

Motor skill learning is characterized by improved performance and reduced motor variability. The neural mechanisms that couple skill level and variability, however, are not known. The zebra finch, a songbird, presents a unique opportunity to address this question because production of learned song and induction of vocal variability are instantiated in distinct circuits that converge on a motor cortex analogue controlling vocal output. To probe the interplay between learning and variability, we made intracellular recordings from neurons in this area, characterizing how their inputs from the functionally distinct pathways change throughout song development. We found that inputs that drive stereotyped song-patterns are strengthened and pruned, while inputs that induce variability remain unchanged. A simple network model showed that strengthening and pruning of action-specific connections reduces the sensitivity of motor control circuits to variable input and neural ‘noise’. This identifies a simple and general mechanism for learning-related regulation of motor variability. DOI: http://dx.doi.org/10.7554/eLife.03697.00

Fast non-negative deconvolution for spike train inference from population calcium imaging

Calcium imaging for observing spiking activity from large populations of neurons are quickly gaining popularity. While the raw data are fluorescence movies, the underlying spike trains are of interest. This work presents a fast non-negative deconvolution filter to infer the approximately most likely spike train for each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm is fast enough that even when imaging over 100 neurons, inference can be performed on the set of all observed traces faster than real-time. Performing optimal spatial filtering on the images further refines the estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments.Comment: 22 pages, 10 figure

Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity

Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent “triplet” model of STDP. Our results indicate that the detailed shape of the STDP window function near the transition from depression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study

Network Structures Arising from Spike-Timing Dependent Plasticity

Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains, and organizes neural circuits in functionally useful ways. In this dissertation, I study the structures arising from STDP in a population of synapses with an emphasis on the interplay between synaptic stability and Hebbian competition, explained in Chapter 1. Starting from the simplest description of STDP which relates synaptic modification to the intervals between pairs of pre- and postsynaptic spikes, I show in Chapter 2 that stability and Hebbian competition are incompatible in this class of ``pair-based'' STDP models, either when hard bounds or soft bounds are imposed to the synapses. In chapter 3, I propose an alternative biophysically inspired method for imposing bounds to synapses, i.e. introducing a small temporal shift in the STDP window. Shifted STDP overcomes the incompatibility of synaptic stability and competition and can implement both Hebbian and anti-Hebbian forms of competitive plasticity. In light of experiments the explored a variety of spike patterns, STDP models have been augmented to account for interactions between multiple pre- and postsynaptic action potentials. In chapter 4, I study the stability/competition interplay in three different proposed multi-spike models of STDP. I show that the ``triplet model'' leads to a partially steady-state distribution of synaptic weights and induces Hebbian competition. The ``suppression model'' develops a stable distribution of weights when the average weight is high and shows predominantly anti-Hebbian competition. The "NMDAR-based" model can lead to either stable or partially stable synaptic weight distribution and exhibits both Hebbian and anti-Hebbian competition, depending on the parameters. I conclude that multi-spike STDP models can produce radically different effects at the population level depending on how they implement multi-spike interactions. Finally in chapter 5, I focus on the types of global structures that arise from STDP in a recurrent network. By analyzing pairwise interactions of neurons through STDP and also numerical simulations of a large network, I show that conventional pair-based STDP functions as a loop-eliminating mechanism in a network of spiking neurons and organizes neurons into in- and out-hubs. Loop-elimination increases when depression dominates and decreases when potentiation dominates. STDP with dominant depression implements a buffering mechanism for network firing rates, and shifted STDP can generate recurrent connections in a network, and also functions as a homeostatic mechanism that maintains a roughly constant average value of the synaptic strengths. In conclusion, studying pairwise interactions of neurons through STDP provides a number of important insights about the structures that arise from this plasticity rule in large networks. This approach can be extended to networks with more complex STDP models and more structured external input

Dynamics of reciprocal synapses with rightward shifted STDP.

<p><b>A.</b> When the baseline firing rates of the two neurons are 1.8 Hz, a saddle node exists out of the allowed range, schematically illustrated at the top right. Arrows show the movement of trajectories. Initial conditions starting within the red area end up at the attractor at the top right corner, which corresponds to strong recurrent connections. This increases the baseline firing rate of the embedding network and pushes the network into the regime shown in B. <b>B.</b> When the baseline firing rates of the two neurons are 37 Hz, a single stable fixed point exists within the allowed range of synaptic weights. All initial conditions end up at this fixed point, resulting in a recurrent reciprocal connection. <b>C.</b> When the baseline firing rates of the two neurons are 50 Hz, a stable fixed point exists out of the allowed range, schematically illustrated at the bottom left. Movement of trajectories toward the stable fixed point results in connectivity loss, regardless of the initial condition. This effect reduces the rate of the embedding network and pushes the system into the regime shown in B. It is not necessary to impose upper bounds in this case, so they are depicted as dotted lines.</p

Stability and competition in the suppression model.

<p><b>A.</b> Fixed points of ⟨<i>w</i>⟩ as functions of the ratio between the potentiation and depression time constants. The stable fixed point disappears beyond the critical value <i>τ</i>₊/<i>τ</i>₋ < 1.2. When the ratio approaches the critical value, the fixed point grows rapidly (gray area), leading to a stable distribution. <b>B.</b> The average drift when <i>τ</i>₊/<i>τ</i>₋ = 1. The solid curve shows the analytical result (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004750#pcbi.1004750.e018" target="_blank">Eq 6</a>) and the boundaries of gray shading is obtained by simulations. The filled circle is the stable fixed point. <b>C.</b> The average drift when <i>τ</i>₊/<i>τ</i>₋ = 1.1. The stable fixed point moves to larger values than in B. <b>D.</b> The average drift when <i>τ</i>₊/<i>τ</i>₋ = 1.5. No nontrivial fixed point exists. <b>E.</b> The partially stable bimodal steady-state distribution of weights corresponding to the parameters of B. <b>F.</b> The stable steady-state distribution of weights corresponding to the parameters of C. <b>G.</b> The unstable steady-state distribution of weights clustered around the upper bound corresponding to the parameters of D, when no stable fixed point exists. <b>H-J.</b> Competition between correlated and uncorrelated synapses with parameter corresponding to E-G. The competition is anti-Hebbian in all cases.</p

Neuronal, synaptic, and plasticity parameters.

<p>Neuronal, synaptic, and plasticity parameters.</p