Robert R. Kerr

Delay Selection by Spike-Timing-Dependent Plasticity in Recurrent Networks of Spiking Neurons Receiving Oscillatory Inputs

Learning rules, such as spike-timing-dependent plasticity (STDP), change the structure of networks of neurons based on the firing activity. A network level understanding of these mechanisms can help infer how the brain learns patterns and processes information. Previous studies have shown that STDP selectively potentiates feed-forward connections that have specific axonal delays, and that this underlies behavioral functions such as sound localization in the auditory brainstem of the barn owl. In this study, we investigate how STDP leads to the selective potentiation of recurrent connections with different axonal and dendritic delays during oscillatory activity. We develop analytical models of learning with additive STDP in recurrent networks driven by oscillatory inputs, and support the results using simulations with leaky integrate-and-fire neurons. Our results show selective potentiation of connections with specific axonal delays, which depended on the input frequency. In addition, we demonstrate how this can lead to a network becoming selective in the amplitude of its oscillatory response to this frequency. We extend this model of axonal delay selection within a single recurrent network in two ways. First, we show the selective potentiation of connections with a range of both axonal and dendritic delays. Second, we show axonal delay selection between multiple groups receiving out-of-phase, oscillatory inputs. We discuss the application of these models to the formation and activation of neuronal ensembles or cell assemblies in the cortex, and also to missing fundamental pitch perception in the auditory brainstem.

Coexistence of reward and unsupervised learning during the operant conditioning of neural firing rates.

A fundamental goal of neuroscience is to understand how cognitive processes, such as operant conditioning, are performed by the brain. Typical and well studied examples of operant conditioning, in which the firing rates of individual cortical neurons in monkeys are increased using rewards, provide an opportunity for insight into this. Studies of reward-modulated spike-timing-dependent plasticity (RSTDP), and of other models such as R-max, have reproduced this learning behavior, but they have assumed that no unsupervised learning is present (i.e., no learning occurs without, or independent of, rewards). We show that these models cannot elicit firing rate reinforcement while exhibiting both reward learning and ongoing, stable unsupervised learning. To fix this issue, we propose a new RSTDP model of synaptic plasticity based upon the observed effects that dopamine has on long-term potentiation and depression (LTP and LTD). We show, both analytically and through simulations, that our new model can exhibit unsupervised learning and lead to firing rate reinforcement. This requires that the strengthening of LTP by the reward signal is greater than the strengthening of LTD and that the reinforced neuron exhibits irregular firing. We show the robustness of our findings to spike-timing correlations, to the synaptic weight dependence that is assumed, and to changes in the mean reward. We also consider our model in the differential reinforcement of two nearby neurons. Our model aligns more strongly with experimental studies than previous models and makes testable predictions for future experiments.

Minimizing activation of overlying axons with epiretinal stimulation: The role of fiber orientation and electrode configuration

Currently, a challenge in electrical stimulation of the retina with a visual prosthesis (bionic eye) is to excite only the cells lying directly under the electrode in the ganglion cell layer, while avoiding excitation of axon bundles that pass over the surface of the retina in the nerve fiber layer. Stimulation of overlying axons results in irregular visual percepts, limiting perceptual efficacy. This research explores how differences in fiber orientation between the nerve fiber layer and ganglion cell layer leads to differences in the electrical activation of the axon initial segment and axons of passage. Approach. Axons of passage of retinal ganglion cells in the nerve fiber layer are characterized by a narrow distribution of fiber orientations, causing highly anisotropic spread of applied current. In contrast, proximal axons in the ganglion cell layer have a wider distribution of orientations. A four-layer computational model of epiretinal extracellular stimulation that captures the effect of neurite orientation in anisotropic tissue has been developed using a volume conductor model known as the cellular composite model. Simulations are conducted to investigate the interaction of neural tissue orientation, stimulating electrode configuration, and stimulation pulse duration and amplitude. Main results. Our model shows that simultaneous stimulation with multiple electrodes aligned with the nerve fiber layer can be used to achieve selective activation of axon initial segments rather than passing fibers. This result can be achieved while reducing required stimulus charge density and with only modest increases in the spread of activation in the ganglion cell layer, and is shown to extend to the general case of arbitrary electrode array positioning and arbitrary target volume. Significance. These results elucidate a strategy for more targeted stimulation of retinal ganglion cells with experimentally-relevant multi-electrode geometries and achievable stimulation requirements.

A computational model of orientation-dependent activation of retinal ganglion cells

Currently, a challenge in electrical stimulation for epiretinal prostheses is the avoidance of stimulation of axons of passage in the nerve fiber layer that originate from distant regions of the ganglion cell layer. A computational model of extracellular stimulation that captures the effect of neurite orientation in anisotropic tissue is developed using a modified version of the standard volume conductor model, known as the cellular composite model, embedded in a four layer model of the retina. Simulations are conducted to investigate the interaction of neural tissue orientation, electrode placement, and stimulation pulse duration and amplitude. Using appropriate multiple electrode configurations and higher frequency stimulation, preferential activation of the axon initial segment is shown to be possible for a range of realistic electrode-retina separation distances. These results establish a quantitative relationship between the time-course of stimulation and physical properties of the tissue, such as fiber orientation.

Goal-directed control with cortical units that are gated by both top-down feedback and oscillatory coherence

The brain is able to flexibly select behaviors that adapt to both its environment and its present goals. This cognitive control is understood to occur within the hierarchy of the cortex and relies strongly on the prefrontal and premotor cortices [1], which sit at the top of this hierarchy. Pyramidal neurons, the principal neurons that form the basis of the functional circuits in the cortex, have been observed to exhibit much stronger responses when they receive inputs at their soma/basal dendrites that are coincident with inputs at their apical dendrites [2]. This corresponds to receiving inputs simultaneously from both higher-order regions (feedback) and lower-order regions (feedforward) [3]. In addition to this, temporal coherence between oscillations, such as gamma oscillations, in different neuronal groups has been proposed to modulate and route communication in the brain [4]. In this study, we develop a simple, but novel, neural mass model in which cortical units (or ensembles) of pyramidal neurons and inhibitory interneurons exhibit gamma oscillations when they receive coherent oscillatory inputs from both feedforward and feedback connections. In this way, the activity of these units is gated by both top-down feedback and oscillatory coherence. We demonstrate how these units can be connected into circuits to perform logic operations (e.g., A OR B OR C) and identify the different ways in which these operations can be initiated and manipulated by top-down feedback. We show that more sophisticated and flexible top-down control is possible when the gain of units is modulated by not only top-down feedback but by oscillatory coherence. Specifically, it is possible to not only add units to, or remove units from, the operation of a higher-level unit using top-down feedback, but it is also possible to modify the type of role that a unit plays in the operation. Finally, we explore how different network properties affect top-down control and processing in large networks. Based on this, we make predictions about the likely connectivities between certain brain regions and relate our findings to those of experimental studies, where neurons in different cortical regions are recorded during goal-directed, behavioral tasks [1].

Requirements for the robust operant conditioning of neural firing rates

Operant conditioning experiments have shown that changes in the firing rates of individual neurons in the motor cortex of monkeys can be elicited [1,2]. In these experiments, the firing rate of the neurons were measured using an implanted electrode, and the monkeys were presented with feedback based on these rates and rewarded for increasing them. Behavioral learning such as this is assumed to be due to plasticity at the synaptic level and reward-modulated spike-timing-dependent plasticity (RSTDP) has previously been proposed as such a model [3]. In this study, we propose a generalization of the existing RSTDP model (classical RSTDP) that can account for experiments where dopamine differentially modulates the amplitude of long-term potentiation and depression (LTP and LTD) [4]. Using analytical techniques and numerical simulations with leaky integrate-and-fire (LIF) neurons, we compare the classical RSTDP (see Figure ​Figure1A)1A) with our generalized model (see Figure ​Figure1B).1B). We consider the potential for these models to elicit the increased firing rates observed in operant conditioning experiments [1,2] and find two requirements. The first requirement is that, relative to their base level amplitudes, the strengthening of LTP by the reward signal must be greater than the strengthening of LTD. Classical RSTDP cannot exhibit this and, contrary to previous studies [3], we predict that it consequently cannot robustly elicit an increased firing rate. The second requirement is that the reinforced neuron must be able to exhibit short inter-spike intervals (ISIs) relative to its mean ISI. For the LIF neurons we consider, this corresponds to being in a fluctuation-driven regime, such as receiving a balance of excitatory and inhibitory inputs. The findings of this study are consistent with existing experimental studies and they also make testable predictions for possible future experiments. Figure 1 Effective STDP learning windows that show the synaptic change, ΔK, caused by a spike pair with the timing difference, Δt, between the pre- and post-synaptic spikes. The different windows are for different reward signal levels (y = 0, 1, ...

STDP encodes oscillation frequencies in the connections of recurrent networks of spiking neurons

Spike-timing-dependent plasticity (STDP) is a learning rule that updates synaptic strengths based on the relative timing of pre- and post-synaptic spikes. Unlike rate-based Hebbian learning, STDP can potentially encode fast temporal correlations in neuronal activity, such as oscillations, in the functional structure of networks of neurons that have axonal and dendritic propagation delays. The motivation behind this study was to understand the different ways that spatiotemporal patterns can be learnt by the recurrent connections in a network of neurons with STDP present. This understanding is vital to uncovering the mechanisms by which basic learning and information processing tasks are performed throughout the brain. A specific example in which these mechanisms may contribute is in explaining how the brain can perceive the pitch of complex sounds up to 300Hz. This work employs and builds upon the analytical framework for learning with STDP used in a previous study [1]. In this study, the changes made by additive STDP to synaptic strengths in recurrent networks with axonal delays receiving oscillatory inputs were investigated analytically with the Poisson neuron model and verified through simulations with leaky integrate-and-fire (LIF) neurons. Frequencies between 100-300Hz were considered, which correspond to the modulation frequencies found in the auditory brainstem representing the fundamental frequency of different natural sounds. The analysis and simulations found that connections were selectively potentiated and depressed based on their axonal delay in such a way that the delays of the strong connections in the network “resonated” with the input frequency (Figure ​(Figure1A).1A). The trained networks were found to respond selectively to the frequency they were trained with (Figure ​(Figure1B).1B). Higher frequencies (e.g. 240Hz as shown here) would always be learnt by the network, but in order to show a selective response after learning they needed faster neuronal and synaptic time constants (see details in Figure ​Figure11 caption). Figure 1 Results of simulations with networks of 10,000 LIF neurons. A: The mean synaptic weight with axonal delay of a network before learning (dashed: all weights initially set to 0.0025 with an even spread of delays over 1-10ms) and after learning for 20,000s ...