Modeling Pharmacological Clock and Memory Patterns of Interval Timing in a Striatal Beat-Frequency Model with Realistic, Noisy Neurons

In most species, the capability of perceiving and using the passage of time in the seconds-to-minutes range (interval timing) is not only accurate but also scalar: errors in time estimation are linearly related to the estimated duration. The ubiquity of scalar timing extends over behavioral, lesion, and pharmacological manipulations. For example, in mammals, dopaminergic drugs induce an immediate, scalar change in the perceived time (clock pattern), whereas cholinergic drugs induce a gradual, scalar change in perceived time (memory pattern). How do these properties emerge from unreliable, noisy neurons firing in the milliseconds range? Neurobiological information relative to the brain circuits involved in interval timing provide support for an striatal beat frequency (SBF) model, in which time is coded by the coincidental activation of striatal spiny neurons by cortical neural oscillators. While biologically plausible, the impracticality of perfect oscillators, or their lack thereof, questions this mechanism in a brain with noisy neurons. We explored the computational mechanisms required for the clock and memory patterns in an SBF model with biophysically realistic and noisy Morris–Lecar neurons (SBF–ML). Under the assumption that dopaminergic drugs modulate the firing frequency of cortical oscillators, and that cholinergic drugs modulate the memory representation of the criterion time, we show that our SBF–ML model can reproduce the pharmacological clock and memory patterns observed in the literature. Numerical results also indicate that parameter variability (noise) – which is ubiquitous in the form of small fluctuations in the intrinsic frequencies of neural oscillators within and between trials, and in the errors in recording/retrieving stored information related to criterion time – seems to be critical for the time-scale invariance of the clock and memory patterns

Phase resetting and its implications for interval timing with intruders

AbstractTime perception in the second-to-minutes range is crucial for fundamental cognitive processes like decision making, rate calculation, and planning. We used a striatal beat frequency (SBF) computational model to predict the response of an interval timing network to intruders, such as gaps in conditioning stimulus (CS), or distracters presented during the uninterrupted CS. We found that, depending on the strength of the input provided to neural oscillators by the intruder, the SBF model can either ignore it or reset timing. The significant delays in timing produced by emotionally charged distracters were numerically simulated by a strong phase resetting of all neural oscillators involved in the SBF network for the entire duration of the evoked response. The combined effect of emotional distracter and pharmacological manipulations was modeled in our SBF model by modulating the firing frequencies of neural oscillators after they are released from inhibition due to emotional distracters.This article is part of a Special Issue entitled: SI: Associative and Temporal Learning

A Population-Based Model of the Temporal Memory in the Hippocampus

Spatial and temporal dimensions are fundamental for orientation, adaptation, and survival of organisms. Hippocampus has been identified as the main neuroanatomical structure involved both in space and time perception and their internal representation. Dorsal hippocampus lesions showed a leftward shift (toward shorter durations) in peak-interval procedures, whereas ventral lesions shifted the peak time toward longer durations. We previously explained hippocampus lesion experimental findings by assuming a topological map model of the hippocampus with shorter durations memorized ventrally and longer durations more dorsal. Here we suggested a possible connection between the abstract topological maps model of the hippocampus that stored reinforcement times in a spatially ordered memory register and the “time cells” of the hippocampus. In this new model, the time cells provide a uniformly distributed time basis that covers the entire to-be-learned temporal duration. We hypothesized that the topological map of the hippocampus stores the weights that reflect the contribution of each time cell to the average temporal field that determines the behavioral response. The temporal distance between the to-be-learned criterion time and the time of the peak activity of each time cell provides the error signal that determines the corresponding weight correction. Long-term potentiation/depression could enhance/weaken the weights associated to the time cells that peak closer/farther to the criterion time. A coincidence detector mechanism, possibly under the control of the dopaminergic system, could be involved in our suggested error minimization and learning algorithm

Low-dimensional attractor for neural activity from local field potentials in optogenetic mice

We used optogenetic mice to investigate possible nonlinear responses of the medial prefrontal cortex (mPFC) local network to light stimuli delivered by a 473 nm laser through a fiber optics. Every 2 s, a brief 10 ms light pulse was applied and the local field potentials (LFPs) were recorded with a 10 kHz sampling rate. The experiment was repeated 100 times and we only retained and analyzed data from six animals that showed stable and repeatable response to optical stimulations. The presence of nonlinearity in our data was checked using the null hypothesis that the data were linearly correlated in the temporal domain, but were random otherwise. For each trail, 100 surrogate data sets were generated and both time reversal asymmetry and false nearest neighbor (FNN) were used as discriminating statistics for the null hypothesis. We found that nonlinearity is present in all LFP data. The first 0.5 s of each 2 s LFP recording were dominated by the transient response of the networks. For each trial, we used the last 1.5 s of steady activity to measure the phase resetting induced by the brief 10 ms light stimulus. After correcting the LFPs for the effect of phase resetting, additional preprocessing was carried out using dendrograms to identify ``similar'' groups among LFP trials. We found that the steady dynamics of mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar ``8''-shaped attractors across different animals. Our results also open the possibility of designing a low-dimensional model for optical stimulation of the mPFC local network

Inactivation of the Medial-Prefrontal Cortex Impairs Interval Timing Precision, but Not Timing Accuracy or Scalar Timing in a Peak-Interval Procedure in Rats

Motor sequence learning, planning and execution of goal-directed behaviors, and decision making rely on accurate time estimation and production of durations in the seconds-to-minutes range. The pathways involved in planning and execution of goal-directed behaviors include cortico-striato-thalamo-cortical circuitry modulated by dopaminergic inputs. A critical feature of interval timing is its scalar property, by which the precision of timing is proportional to the timed duration. We examined the role of medial prefrontal cortex (mPFC) in timing by evaluating the effect of its reversible inactivation on timing accuracy, timing precision and scalar timing. Rats were trained to time two durations in a peak-interval (PI) procedure. Reversible mPFC inactivation using GABA agonist muscimol resulted in decreased timing precision, with no effect on timing accuracy and scalar timing. These results are partly at odds with studies suggesting that ramping prefrontal activity is crucial to timing but closely match simulations with the Striatal Beat Frequency (SBF) model proposing that timing is coded by the coincidental activation of striatal neurons by cortical inputs. Computer simulations indicate that in SBF, gradual inactivation of cortical inputs results in a gradual decrease in timing precision with preservation of timing accuracy and scalar timing. Further studies are needed to differentiate between timing models based on coincidence detection and timing models based on ramping mPFC activity, and clarify whether mPFC is specifically involved in timing, or more generally involved in attention, working memory, or response selection/inhibition

Predicting phase resetting due to multiple stimuli

We generalized the phase resetting curve (PRC) to a more realistic case of neural oscillators receiving two or more inputs per cycle. The PRC tabulates the transient change in the firing period of a neuron due to an external perturbation, such as a presynaptic stimulus. We used a conductance-based model neuron to estimate experimentally the two-stimulus PRC and compared the results against our mathematical prediction based on the assumption of instantaneous recurrent stimulation. Within the limits of the recurrent stimulation assumptions, we found that the newly introduced prediction for the two-stimulus PRC matched experimental measurements. Our new results open the possibility of a more realistic approach to predicting phase-locked modes in neural networks, such as the synchronous activity of large networks during epileptic seizures