Precision estimation and second-order prediction errors in cortical circuits

Minimization of cortical prediction errors is believed to be a key canonical computation of the cerebral cortex underlying perception, action and learning. However, it is still unclear how the cortex should form and use knowledge about uncertainty in this process of prediction error minimization. Here we derive neural dynamics minimizing prediction errors under the assumption that cortical areas must not only predict the activity in other areas and sensory streams, but also jointly estimate the precision of their predictions. This leads to a dynamic modulatory balancing of cortical streams based on context-dependent precision estimates. Moreover, the theory predicts the existence of second-order prediction errors, i.e. errors on precision estimates, computed and propagated through the cortical hierarchy alongside classical prediction errors. These second-order errors are used to learn weights of synapses responsible for precision estimation through an error-correcting synaptic learning rule. Finally, we propose a mapping of the theory to cortical circuitry

Interplay between phosphorylation and palmitoylation mediates plasma membrane targeting and sorting of GAP43.

Phosphorylation and lipidation provide posttranslational mechanisms that contribute to the distribution of cytosolic proteins in growing nerve cells. The growth-associated protein GAP43 is susceptible to both phosphorylation and S-palmitoylation and is enriched in the tips of extending neurites. However, how phosphorylation and lipidation interplay to mediate sorting of GAP43 is unclear. Using a combination of biochemical, genetic, and imaging approaches, we show that palmitoylation is required for membrane association and that phosphorylation at Ser-41 directs palmitoylated GAP43 to the plasma membrane. Plasma membrane association decreased the diffusion constant fourfold in neuritic shafts. Sorting to the neuritic tip required palmitoylation and active transport and was increased by phosphorylation-mediated plasma membrane interaction. Vesicle tracking revealed transient association of a fraction of GAP43 with exocytic vesicles and motion at a fast axonal transport rate. Simulations confirmed that a combination of diffusion, dynamic plasma membrane interaction and active transport of a small fraction of GAP43 suffices for efficient sorting to growth cones. Our data demonstrate a complex interplay between phosphorylation and lipidation in mediating the localization of GAP43 in neuronal cells. Palmitoylation tags GAP43 for global sorting by piggybacking on exocytic vesicles, whereas phosphorylation locally regulates protein mobility and plasma membrane targeting of palmitoylated GAP43

Dendrites help mitigate the plasticity-stability dilemma

Abstract With Hebbian learning ‘who fires together wires together’, well-known problems arise. Hebbian plasticity can cause unstable network dynamics and overwrite stored memories. Because the known homeostatic plasticity mechanisms tend to be too slow to combat unstable dynamics, it has been proposed that plasticity must be highly gated and synaptic strengths limited. While solving the issue of stability, gating and limiting plasticity does not solve the stability-plasticity dilemma. We propose that dendrites enable both stable network dynamics and considerable synaptic changes, as they allow the gating of plasticity in a compartment-specific manner. We investigate how gating plasticity influences network stability in plastic balanced spiking networks of neurons with dendrites. We compare how different ways to gate plasticity, namely via modulating excitability, learning rate, and inhibition increase stability. We investigate how dendritic versus perisomatic gating allows for different amounts of weight changes in stable networks. We suggest that the compartmentalisation of pyramidal cells enables dendritic synaptic changes while maintaining stability. We show that the coupling between dendrite and soma is critical for the plasticity-stability trade-off. Finally, we show that spatially restricted plasticity additionally improves stability

Inhibition as a Binary Switch for Excitatory Plasticity in Pyramidal Neurons.

Synaptic plasticity is thought to induce memory traces in the brain that are the foundation of learning. To ensure the stability of these traces in the presence of further learning, however, a regulation of plasticity appears beneficial. Here, we take up the recent suggestion that dendritic inhibition can switch plasticity of excitatory synapses on and off by gating backpropagating action potentials (bAPs) and calcium spikes, i.e., by gating the coincidence signals required for Hebbian forms of plasticity. We analyze temporal and spatial constraints of such a gating and investigate whether it is possible to suppress bAPs without a simultaneous annihilation of the forward-directed information flow via excitatory postsynaptic potentials (EPSPs). In a computational analysis of conductance-based multi-compartmental models, we demonstrate that a robust control of bAPs and calcium spikes is possible in an all-or-none manner, enabling a binary switch of coincidence signals and plasticity. The position of inhibitory synapses on the dendritic tree determines the spatial extent of the effect and allows a pathway-specific regulation of plasticity. With appropriate timing, EPSPs can still trigger somatic action potentials, although backpropagating signals are abolished. An annihilation of bAPs requires precisely timed inhibition, while the timing constraints are less stringent for distal calcium spikes. We further show that a wide-spread motif of local circuits-feedforward inhibition-is well suited to provide the temporal precision needed for the control of bAPs. Altogether, our model provides experimentally testable predictions and demonstrates that the inhibitory switch of plasticity can be a robust and attractive mechanism, hence assigning an additional function to the inhibitory elements of neuronal microcircuits beyond modulation of excitability

Disinhibition by VIP interneurons is orthogonal to cross-modal attentional modulation in primary visual cortex.

Attentional modulation of sensory processing is a key feature of cognition; however, its neural circuit basis is poorly understood. A candidate mechanism is the disinhibition of pyramidal cells through vasoactive intestinal peptide (VIP) and somatostatin (SOM)-positive interneurons. However, the interaction of attentional modulation and VIP-SOM disinhibition has never been directly tested. We used all-optical methods to bi-directionally manipulate VIP interneuron activity as mice performed a cross-modal attention-switching task. We measured the activities of VIP, SOM, and parvalbumin (PV)-positive interneurons and pyramidal neurons identified in the same tissue and found that although activity in all cell classes was modulated by both attention and VIP manipulation, their effects were orthogonal. Attention and VIP-SOM disinhibition relied on distinct patterns of changes in activity and reorganization of interactions between inhibitory and excitatory cells. Circuit modeling revealed a precise network architecture consistent with multiplexing strong yet non-interacting modulations in the same neural population

Compartment-specific inhibition of bAPs and calcium spikes during BAC firing.

<p>A: Effect of inhibition locus on dendritic coincidence signals, when somatic current injection was paired with dendritic excitation (with a delay Δt of 0 ms) to trigger a calcium spike (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004768#pcbi.1004768.g001" target="_blank">Fig 1D</a>). As in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004768#pcbi.1004768.g003" target="_blank">Fig 3A</a>, the recording site varies along the rows; the site of inhibition varies along the columns. Inhibitory conductance is indicated by the blue traces (inhibition onset was 1.5 ms after stimulation onset.). a: No inhibition. b: Distal inhibition (460 μm, 50 nS) suppressed the calcium spike (I) and thus distal plasticity, but left signaling in the remaining dendritic tree intact (II and III). c: Proximal inhibition (90 μm, 50 nS) affected signaling in the whole apical dendrite by eliminating the bAP (II), and thus the calcium spike (I), but did not affect the bAP in the basal dendrite (III). d: In the presence of a calcium-spike induced somatic burst, one inhibitory pulse was not sufficient to block the propagation of all bAPs into the basal dendrite (III). e: The train of bAPs in the basal dendrite, and thus basal plasticity, was suppressed by four inhibitory conductance changes at a frequency of 75 Hz on the proximal basal dendrite (100 μm, 70 nS) (III), while apical signaling was unchanged (I and II). B: Inhibition of calcium spikes in the distal apical dendrite. Calcium spikes were triggered by coincident bAPs and distal excitation with a temporal separation (Δt) of 0 ms (as in A). Color-coded is the calcium transient in the apical tuft, normalized to its uninhibited value. While the bAP could be modulated by proximal inhibition within a time window of 1 ms (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004768#pcbi.1004768.g003" target="_blank">Fig 3B</a>), calcium spikes were rather insensitive to timing, and were abolished by weak distal inhibition. C: Inhibition of calcium spikes in the distal apical dendrite, when the neuron was driven by excitatory synapses distributed along the apical trunk to represent inputs from oblique dendrites (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004768#sec019" target="_blank">Methods</a>). The EPSPs were paired with distal excitation with a temporal separation (Δt) of 0 ms. As in B, the calcium spike could be modulated, less dependent on timing than the bAP.</p

Compartment-specific inhibition of bAPs in the absence of calcium spikes.

<p>A: Effect of inhibition locus on bAPs, elicited by somatic current injection. The recording site varies along the rows; the site of inhibition varies along the columns. Inhibitory conductance is indicated by the blue traces (inhibition onset was 1.5 ms after stimulation onset.). a: No inhibition. b: Distal inhibition (460 μm, 50 nS) affected the distal bAP, but did not have a pronounced effect in the absence of a calcium spike (I), it however left signaling in the remaining dendritic tree intact (II and III). c: Proximal inhibition (90 μm, 50 nS) affected signaling in the whole apical dendrite by eliminating the bAP (II), but did not affect the bAP in the basal dendrite (III). d: The bAP in the basal dendrite, and thus basal plasticity, was suppressed by basal inhibition (100 μm, 50 nS) (III), while apical signaling was unchanged (I and II). B: Effect of inhibition onset timing on bAP and calcium spike modulation. Inhibition was shunting with GABA_A time constants (τ_rise = 0.5 ms, τ_decay = 5 ms). Strength of inhibition varies along each y-axis, onset of inhibition relative to the onset of the somatic step current varies along each x-axis. A: Proximal inhibition on the apical dendrite and its effect on bAPs. The corresponding somatic APs were elicited by somatic step current injection (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004768#pcbi.1004768.g001" target="_blank">Fig 1C</a>) and peaked around 2.5 ms after stimulation onset. Color-coded is the amplitude of the bAP measured in the oblique dendrite (star indicates recording site). Unless somatic spiking was inhibited (black), either a full-blown bAP (red) or no bAP (light orange) could be observed. C: The neuron was driven by excitatory synapses distributed along the apical trunk to represent inputs from oblique dendrites (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004768#sec019" target="_blank">Methods</a>). Modulation of the bAP was possible in a narrow time window.</p

Circuit model of feedforward inhibition.

<p>A: Topology of the circuit with a multi-compartment pyramidal neuron model and a model of a fast-spiking inhibitory interneuron (IN, targeting pyramidal neuron) receiving excitatory input from a source (EX) at time t₀ and potentially tonic disinhibition (IN, targeting IN). B: Effect of switching the feedforward interneuron on and off (via a second interneuron—marked gray in panel A) measured in the dendrite of the pyramidal neuron (370 μm from the soma), which in turn is driven by apical excitation. Note that the circuit is identical to that in panel A, although the lefthand schematics only zoom in on the interneurons. Upper paradigm: When the feedforward interneuron is switched off (in gray) because of activation of the second interneuron (in black), excitation triggers a spike in the pyramidal cell’s soma which propagates unhindered into the dendrite. Lower paradigm: When the feedforward interneuron is active (in black) due to excitation and because the second interneuron is switched off (in gray), excitation triggers a spike in the pyramidal cell’s soma that does not propagate far into the dendrite due to the inhibition provided by the feedforward interneuron (90 μm from soma, Δt = 2 ms).</p

Analysis of the effect of inhibition on the backpropagating action potential (bAP) in dependence on inhibitory conductance and dendritic location.

<p>The bAP was triggered by threshold somatic current injection (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004768#pcbi.1004768.g001" target="_blank">Fig 1C</a>). A: Amplitude of the bAP on its path from the soma, along the proximal apical dendrite into the distal oblique dendrite (arrow), normalized to its amplitude at the soma, for different values of inhibition strength (lines in different colors). Inhibition with a double exponential time course (τ_rise = 0.5 ms, τ_decay = 5 ms) was placed on the proximal apical dendrite (90 μm from the soma). Inhibition onset was 2 ms after stimulation onset. The somatic spike peaked around 2.5 ms after stimulation onset. B: Amplitude of the inhibited bAP relative to the non-inhibited bAP as a function of inhibition strength, measured in the distal part of the oblique dendrite (indicated by star in illustration and in A) for different locations of inhibition on the apical trunk (different shades indicate distance to soma in μm, thick line for 90 μm). Inhibition had an all-or-none effect on the bAP.</p