Cooperation of spike timing-dependent and heterosynaptic plasticities in neural networks: a Fokker-Planck approach

The Role of Neuromodulators in Cortical Plasticity. A Computational Perspective

Neuromodulators play a ubiquitous role across the brain in regulating plasticity. With recent advances in experimental techniques, it is possible to study the effects of diverse neuromodulatory states in specific brain regions. Neuromodulators are thought to impact plasticity predominantly through two mechanisms: the gating of plasticity and the upregulation of neuronal activity. However, the consequences of these mechanisms are poorly understood and there is a need for both experimental and theoretical exploration. Here we illustrate how neuromodulatory state affects cortical plasticity through these two mechanisms. First, we explore the ability of neuromodulators to gate plasticity by reshaping the learning window for spike-timing-dependent plasticity. Using a simple computational model, we implement four different learning rules and demonstrate their effects on receptive field plasticity. We then compare the neuromodulatory effects of upregulating learning rate versus the effects of upregulating neuronal activity. We find that these seemingly similar mechanisms do not yield the same outcome: upregulating neuronal activity can lead to either a broadening or a sharpening of receptive field tuning, whereas upregulating learning rate only intensifies the sharpening of receptive field tuning. This simple model demonstrates the need for further exploration of the rich landscape of neuromodulator-mediated plasticity. Future experiments, coupled with biologically detailed computational models, will elucidate the diversity of mechanisms by which neuromodulatory state regulates cortical plasticity.

Spike-timing computation properties of a feed-forward neural network model

Brain function is characterized by dynamical interactions among networks of neurons. These interactions are mediated by network topology at many scales ranging from microcircuits to brain areas. Understanding how networks operate can be aided by understanding how the transformation of inputs depends upon network connectivity patterns, e.g., serial and parallel pathways. To tractably determine how single synapses or groups of synapses in such pathways shape these transformations, we modeled feed-forward networks of 7–22 neurons in which synaptic strength changed according to a spike-timing dependent plasticity (STDP) rule. We investigated how activity varied when dynamics were perturbed by an activity-dependent electrical stimulation protocol (spike-triggered stimulation; STS) in networks of different topologies and background input correlations. STS can successfully reorganize functional brain networks in vivo, but with a variability in effectiveness that may derive partially from the underlying network topology. In a simulated network with a single disynaptic pathway driven by uncorrelated background activity, structured spike-timing relationships between polysynaptically connected neurons were not observed. When background activity was correlated or parallel disynaptic pathways were added, however, robust polysynaptic spike timing relationships were observed, and application of STS yielded predictable changes in synaptic strengths and spike-timing relationships. These observations suggest that precise input-related or topologically induced temporal relationships in network activity are necessary for polysynaptic signal propagation. Such constraints for polysynaptic computation suggest potential roles for higher-order topological structure in network organization, such as maintaining polysynaptic correlation in the face of relatively weak synapses.

Purinergic receptor- and gap junction-mediated intercellular signalling as a mechanism of heterosynaptic metaplasticity

Synaptic plasticity is subject to activity-dependent long-term modification (metaplasticity). We have recently described a novel form of heterosynaptic metaplasticity in hippocampal CA1, whereby 'priming' activity at one set of synapses confers a metaplastic state that inhibits subsequent LTP both within and between dendritic compartments. Here, we investigated the roles of purinergic signalling and gap junctions in mediating this long-distance communication between synapses. We found that the heterosynaptic metaplasticity requires the hydrolysis of extracellular ATP to adenosine, and activation of adenosine A2, but not A1 receptors. The metaplasticity was also blocked by the non-selective gap junction blockers carbenoxolone and meclofenamic acid, and by a connexin43-specific mimetic peptide. These results indicate that an intercellular signalling cascade underlies the long-distance communication required for this form of metaplasticity.

Approximating distributions in stochastic learning

On-line machine learning algorithms, many biological spike-timing-dependent plasticity (STDP) learning rules, and stochastic neural dynamics evolve by Markov processes. A complete description of such systems gives the probability densities for the variables. The evolution and equilibrium state of these densities are given by a Chapman-Kolmogorov equation in discrete time, or a master equation in continuous time. These formulations are analytically intractable for most cases of interest, and to make progress a nonlinear Fokker-Planck equation (FPE) is often used in their place. The FPE is limited, and some argue that its application to describe jump processes (such as in these problems) is fundamentally flawed. We develop a well-grounded perturbation expansion that provides approximations for both the density and its moments. The approach is based on the system size expansion in statistical physics (which does not give approximations for the density), but our simple development makes the methods accessible and invites application to diverse problems. We apply the method to calculate the equilibrium distributions for two biologically-observed STDP learning rules and for a simple nonlinear machine-learning problem. In all three examples, we show that our perturbation series provides good agreement with Monte-Carlo simulations in regimes where the FPE breaks down.

Adaptive oscillator networks with conserved overall coupling: sequential firing and near-synchronized states

Motivated by recent observations in neuronal systems we investigate all-to-all networks of nonidentical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all incoming links is conserved. We find multiple phase-locked states that fall into two classes: near-synchronized states and splay states. Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given by the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator. In sufficiently large networks the adaptive coupling is found to develop effective network topologies dominated by one or two loops. This results in a multitude of stable splay states, which differ in their firing sequences. With increasing coupling strength their frequency increases linearly and the oscillators become less synchronized. The essential features of the two classes of states are captured analytically in perturbation analyses of the extended Kuramoto model used in the simulations.

A neural circuit model of emotional learning using two pathways with different granularity and speed of information processing

We propose a neural circuit model of emotional learning using two pathways with different granularity and speed of information processing. In order to derive a precise time process, we utilized a spiking model neuron proposed by Izhikevich and spike-timing-dependent synaptic plasticity (STDP) of both excitatory and inhibitory synapses. We conducted computer simulations to evaluate the proposed model. We demonstrate some aspects of emotional learning from the perspective of the time process. The agreement of the results with the previous behavioral experiments suggests that the structure and learning process of the proposed model are appropriate.

A neural circuit model forming semantic network with exception using spike-timing-dependent plasticity of inhibitory synapses

We propose a neural circuit model forming a semantic network with exceptions using the spike-timing-dependent plasticity (STDP) of inhibitory synapses. To evaluate the proposed model, we conducted nine types of computer simulation by combining the three STDP rules for inhibitory synapses and the three spike pairing rules. The simulation results obtained with the STDP rule for inhibitory synapses by Haas et al. [Haas, J.S., Nowotny, T., Abarbanel, H.D.I., 2006, Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. J. Neurophysiol. 96, 3305-3313] are successful, whereas, the other results are unsuccessful. The results and examinations suggested that the inhibitory connection from the concept linked with an exceptional feature to the general feature is necessary for forming a semantic network with an exception.