Pathological cell assembly dynamics in a striatal MSN network model.

Under normal conditions the principal cells of the striatum, medium spiny neurons (MSNs), show structured cell assembly activity patterns which alternate sequentially over exceedingly long timescales of many minutes. It is important to understand this activity since it is characteristically disrupted in multiple pathologies, such as Parkinson's disease and dyskinesia, and thought to be caused by alterations in the MSN to MSN lateral inhibitory connections and in the strength and distribution of cortical excitation to MSNs. To understand how these long timescales arise we extended a previous network model of MSN cells to include synapses with short-term plasticity, with parameters taken from a recent detailed striatal connectome study. We first confirmed the presence of sequentially switching cell clusters using the non-linear dimensionality reduction technique, Uniform Manifold Approximation and Projection (UMAP). We found that the network could generate non-stationary activity patterns varying extremely slowly on the order of minutes under biologically realistic conditions. Next we used Simulation Based Inference (SBI) to train a deep net to map features of the MSN network generated cell assembly activity to MSN network parameters. We used the trained SBI model to estimate MSN network parameters from ex-vivo brain slice calcium imaging data. We found that best fit network parameters were very close to their physiologically observed values. On the other hand network parameters estimated from Parkinsonian, decorticated and dyskinetic ex-vivo slice preparations were different. Our work may provide a pipeline for diagnosis of basal ganglia pathology from spiking data as well as for the design pharmacological treatments.

Theta-gamma phase amplitude coupling in a hippocampal CA1 microcircuit.

Phase amplitude coupling (PAC) between slow and fast oscillations is found throughout the brain and plays important functional roles. Its neural origin remains unclear. Experimental findings are often puzzling and sometimes contradictory. Most computational models rely on pairs of pacemaker neurons or neural populations tuned at different frequencies to produce PAC. Here, using a data-driven model of a hippocampal microcircuit, we demonstrate that PAC can naturally emerge from a single feedback mechanism involving an inhibitory and excitatory neuron population, which interplay to generate theta frequency periodic bursts of higher frequency gamma. The model suggests the conditions under which a CA1 microcircuit can operate to elicit theta-gamma PAC, and highlights the modulatory role of OLM and PVBC cells, recurrent connectivity, and short term synaptic plasticity. Surprisingly, the results suggest the experimentally testable prediction that the generation of the slow population oscillation requires the fast one and cannot occur without it.

Ramping activity in the striatum.

Control of the timing of behavior is thought to require the basal ganglia (BG) and BG pathologies impair performance in timing tasks. Temporal interval discrimination depends on the ramping activity of medium spiny neurons (MSN) in the main BG input structure, the striatum, but the underlying mechanisms driving this activity are unclear. Here, we combine an MSN dynamical network model with an action selection system applied to an interval discrimination task. We find that when network parameters are appropriate for the striatum so that slowly fluctuating marginally stable dynamics are intrinsically generated, up and down ramping populations naturally emerge which enable significantly above chance task performance. We show that emergent population activity is in very good agreement with empirical studies and discuss how MSN network dysfunction in disease may alter temporal perception.

Striatal network modeling in Huntington's Disease.

Medium spiny neurons (MSNs) comprise over 90% of cells in the striatum. In vivo MSNs display coherent burst firing cell assembly activity patterns, even though isolated MSNs do not burst fire intrinsically. This activity is important for the learning and execution of action sequences and is characteristically dysregulated in Huntington's Disease (HD). However, how dysregulation is caused by the various neural pathologies affecting MSNs in HD is unknown. Previous modeling work using simple cell models has shown that cell assembly activity patterns can emerge as a result of MSN inhibitory network interactions. Here, by directly estimating MSN network model parameters from single unit spiking data, we show that a network composed of much more physiologically detailed MSNs provides an excellent quantitative fit to wild type (WT) mouse spiking data, but only when network parameters are appropriate for the striatum. We find the WT MSN network is situated in a regime close to a transition from stable to strongly fluctuating network dynamics. This regime facilitates the generation of low-dimensional slowly varying coherent activity patterns and confers high sensitivity to variations in cortical driving. By re-estimating the model on HD spiking data we discover network parameter modifications are consistent across three very different types of HD mutant mouse models (YAC128, Q175, R6/2). In striking agreement with the known pathophysiology we find feedforward excitatory drive is reduced in HD compared to WT mice, while recurrent inhibition also shows phenotype dependency. We show that these modifications shift the HD MSN network to a sub-optimal regime where higher dimensional incoherent rapidly fluctuating activity predominates. Our results provide insight into a diverse range of experimental findings in HD, including cognitive and motor symptoms, and may suggest new avenues for treatment.

Sensory Stream Adaptation in Chaotic Networks.

Implicit expectations induced by predictable stimuli sequences affect neuronal response to upcoming stimuli at both single cell and neural population levels. Temporally regular sensory streams also phase entrain ongoing low frequency brain oscillations but how and why this happens is unknown. Here we investigate how random recurrent neural networks without plasticity respond to stimuli streams containing oddballs. We found the neuronal correlates of sensory stream adaptation emerge if networks generate chaotic oscillations which can be phase entrained by stimulus streams. The resultant activity patterns are close to critical and support history dependent response on long timescales. Because critical network entrainment is a slow process stimulus response adapts gradually over multiple repetitions. Repeated stimuli generate suppressed responses but oddball responses are large and distinct. Oscillatory mismatch responses persist in population activity for long periods after stimulus offset while individual cell mismatch responses are strongly phasic. These effects are weakened in temporally irregular sensory streams. Thus we show that network phase entrainment provides a biologically plausible mechanism for neural oddball detection. Our results do not depend on specific network characteristics, are consistent with experimental studies and may be relevant for multiple pathologies demonstrating altered mismatch processing such as schizophrenia and depression.

Optimal balance of the striatal medium spiny neuron network.

Slowly varying activity in the striatum, the main Basal Ganglia input structure, is important for the learning and execution of movement sequences. Striatal medium spiny neurons (MSNs) form cell assemblies whose population firing rates vary coherently on slow behaviourally relevant timescales. It has been shown that such activity emerges in a model of a local MSN network but only at realistic connectivities of 10 ~ 20% and only when MSN generated inhibitory post-synaptic potentials (IPSPs) are realistically sized. Here we suggest a reason for this. We investigate how MSN network generated population activity interacts with temporally varying cortical driving activity, as would occur in a behavioural task. We find that at unrealistically high connectivity a stable winners-take-all type regime is found where network activity separates into fixed stimulus dependent regularly firing and quiescent components. In this regime only a small number of population firing rate components interact with cortical stimulus variations. Around 15% connectivity a transition to a more dynamically active regime occurs where all cells constantly switch between activity and quiescence. In this low connectivity regime, MSN population components wander randomly and here too are independent of variations in cortical driving. Only in the transition regime do weak changes in cortical driving interact with many population components so that sequential cell assemblies are reproducibly activated for many hundreds of milliseconds after stimulus onset and peri-stimulus time histograms display strong stimulus and temporal specificity. We show that, remarkably, this activity is maximized at striatally realistic connectivities and IPSP sizes. Thus, we suggest the local MSN network has optimal characteristics - it is neither too stable to respond in a dynamically complex temporally extended way to cortical variations, nor is it too unstable to respond in a consistent repeatable way. Rather, it is optimized to generate stimulus dependent activity patterns for long periods after variations in cortical excitation.

Input dependent cell assembly dynamics in a model of the striatal medium spiny neuron network.

The striatal medium spiny neuron (MSN) network is sparsely connected with fairly weak GABAergic collaterals receiving an excitatory glutamatergic cortical projection. Peri-stimulus time histograms (PSTH) of MSN population response investigated in various experimental studies display strong firing rate modulations distributed throughout behavioral task epochs. In previous work we have shown by numerical simulation that sparse random networks of inhibitory spiking neurons with characteristics appropriate for UP state MSNs form cell assemblies which fire together coherently in sequences on long behaviorally relevant timescales when the network receives a fixed pattern of constant input excitation. Here we first extend that model to the case where cortical excitation is composed of many independent noisy Poisson processes and demonstrate that cell assembly dynamics is still observed when the input is sufficiently weak. However if cortical excitation strength is increased more regularly firing and completely quiescent cells are found, which depend on the cortical stimulation. Subsequently we further extend previous work to consider what happens when the excitatory input varies as it would when the animal is engaged in behavior. We investigate how sudden switches in excitation interact with network generated patterned activity. We show that sequences of cell assembly activations can be locked to the excitatory input sequence and outline the range of parameters where this behavior is shown. Model cell population PSTH display both stimulus and temporal specificity, with large population firing rate modulations locked to elapsed time from task events. Thus the random network can generate a large diversity of temporally evolving stimulus dependent responses even though the input is fixed between switches. We suggest the MSN network is well suited to the generation of such slow coherent task dependent response which could be utilized by the animal in behavior.

Sequentially switching cell assemblies in random inhibitory networks of spiking neurons in the striatum.

The striatum is composed of GABAergic medium spiny neurons with inhibitory collaterals forming a sparse random asymmetric network and receiving an excitatory glutamatergic cortical projection. Because the inhibitory collaterals are sparse and weak, their role in striatal network dynamics is puzzling. However, here we show by simulation of a striatal inhibitory network model composed of spiking neurons that cells form assemblies that fire in sequential coherent episodes and display complex identity-temporal spiking patterns even when cortical excitation is simply constant or fluctuating noisily. Strongly correlated large-scale firing rate fluctuations on slow behaviorally relevant timescales of hundreds of milliseconds are shown by members of the same assembly whereas members of different assemblies show strong negative correlation, and we show how randomly connected spiking networks can generate this activity. Cells display highly irregular spiking with high coefficients of variation, broadly distributed low firing rates, and interspike interval distributions that are consistent with exponentially tailed power laws. Although firing rates vary coherently on slow timescales, precise spiking synchronization is absent in general. Our model only requires the minimal but striatally realistic assumptions of sparse to intermediate random connectivity, weak inhibitory synapses, and sufficient cortical excitation so that some cells are depolarized above the firing threshold during up states. Our results are in good qualitative agreement with experimental studies, consistent with recently determined striatal anatomy and physiology, and support a new view of endogenously generated metastable state switching dynamics of the striatal network underlying its information processing operations.

Market reaction to a bid-ask spread change: a power-law relaxation dynamics.

We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.

Forward shift from reverse replay.

In a recent experimental paper Lee et al. (Neuron 51:639-650, 2006) showed that the firing patterns of CA1 complex-spike neurons gradually shifted forward across trials toward prospective goal locations within a recording session over multiple trials. Here we propose a simple model of this result based on the phenomenon of awake sequence reverse replay (Foster and Wilson, Nature 440(7084):615-617, 2006) which occurs when the animal pauses at the reward location. The model is based on the CA3-CA1 anatomy with modulation of CA3-CA1 synaptic plasticity by feedback from CA3 projecting CA1 interneurons. Sequence replays, which are generated in CA3 by removal of subcortical inhibition on CA1 interneurons, are recoded into the synaptic weights of individual CA1 cells. This produces spatially extended CA1 firing fields, whose response provides a value function on experienced paths toward goal locations. Simulations show that the CA1 firing fields show positive movement in center of mass toward reward locations over many trials with negative shift in first few trials, and development of positive skew.

Dynamical model of salience gated working memory, action selection and reinforcement based on basal ganglia and dopamine feedback.

A simple working memory model based on recurrent network activation is proposed and its application to selection and reinforcement of an action is demonstrated as a solution to the temporal credit assignment problem. Reactivation of recent salient cue states is generated and maintained as a type of salience gated recurrently active working memory, while lower salience distractors are ignored. Cue reactivation during the action selection period allows the cue to select an action while its reactivation at the reward period allows the reinforcement of the action selected by the reactivated state, which is necessarily the action which led to the reward being found. A down-gating of the external input during the reactivation and maintenance prevents interference. A double winner-take-all system which selects only one cue and only one action allows the targeting of the cue-action allocation to be modified. This targeting works both to reinforce a correct cue-action allocation and to punish the allocation when cue-action allocations change. Here we suggest a firing rate neural network implementation of this system based on the basal ganglia anatomy with input from a cortical association layer where reactivations are generated by signals from the thalamus. Striatum medium spiny neurons represent actions. Auto-catalytic feedback from a dopamine reward signal modulates three-way Hebbian long term potentiation and depression at the cortical-striatal synapses which represent the cue-action associations. The model is illustrated by the numerical simulations of a simple example--that of associating a cue signal to a correct action to obtain reward after a delay period, typical of primate cue reward tasks. Through learning, the model shows a transition from an exploratory phase where actions are generated randomly, to a stable directed phase where the animal always chooses the correct action for each experienced state. When cue-action allocations change, we show that this is noticed by the model, the incorrect cue-action allocations are punished and the correct ones discovered.