Formalizing the Internal Clock
To truly understand how the brain processes time, we must translate biological mechanisms into computational principles. The "Internal Clock" is not a singular physical entity like a wristwatch; it is a functional property of neural networks. Over the decades, several competing mathematical frameworks have emerged to explain the psychophysics of interval timing—specifically, the scalar property (Weber's Law), which dictates that the variability of a time estimate is proportional to the duration being timed (i.e., we are more precise at timing 1 second than 10 seconds).
The Pacemaker-Accumulator Model (PAM)
The classical Information Process theory, or the Pacemaker-Accumulator Model (PAM), has dominated the field for nearly half a century. It posits three distinct processing stages: a clock, a memory, and a decision stage. The clock consists of a **pacemaker** that emits pulses at a certain frequency. When a signal to start timing occurs, a **switch** closes, allowing these pulses to flow into an **accumulator**, which counts them. The current count represents the elapsed subjective time.
In this framework, dopamine is typically modeled as increasing the pulse frequency of the pacemaker (speeding up the clock). An accelerated pacemaker leads to a higher count for the same objective duration, resulting in overestimation. Serotonin, conversely, might inhibit the switch closure, causing a "leaky" accumulation or a pause in counting, leading to underestimation. While PAM explains a vast amount of behavioral data, it lacks a clear neuroanatomical substrate. Where is the pacemaker? Recent critiques suggest that PAM is a useful high-level abstraction but fails to capture the distributed, dynamic nature of neural firing.
State-Dependent Networks: Timing as a Trajectory
A powerful alternative to PAM is the State-Dependent Network or "Population Clock" theory. In this view, time is encoded not by counting ticks, but by the evolving pattern of activity in a neural network. Imagine a pebble thrown into a pond; the ripples expand in a predictable way. By looking at the pattern of ripples, one can infer how much time has passed since the pebble hit the water. Similarly, neural networks in the cortex and striatum fall into a predictable sequence of states following a stimulus.
Hippocampal time cells are the quintessence of this model. They form a "delay line" or a defined trajectory through state space. The computation of time, then, becomes a problem of pattern recognition: "Is the network in the state associated with 5 seconds?" The speed of the trajectory determines the subjective speed of time. If dopamine increases the excitability of the network, the state trajectory might evolve faster, reaching the "5-second state" sooner—effectively simulating a faster clock without an explicit counter.
The Striatal Beat Frequency (SBF) as a Bridge
The Striatal Beat Frequency (SBF) model, discussed in the previous article, bridges the gap between oscillatory dynamics and state-dependent networks. It is computationally robust because it leverages the massive dimensionality of cortical oscillators. Mathematically, SBF can generate extremely long time intervals (minutes to hours) by combining oscillators with relatively short periods (milliseconds to seconds), much like how two slightly different sound frequencies create a slow "beat."
SBF also inherently accounts for Scalar Timing. The variance in estimating a beat depends on the phase
noise of the underlying oscillators. As time
Drift-Diffusion Models (DDM)
For decision-making tasks involving time (e.g., "Respond when you think 1 second has passed"), Drift-Diffusion Models are often employed. These models assume that evidence accumulates over time toward a decision threshold. The rate of accumulation (drift rate) and the height of the threshold are key variables. In this framework, D1 receptor activation in the direct pathway is thought to increase the drift rate, facilitating faster responses. Conversely, detailed analysis suggests that D2 receptor blockade (haloperidol) raises the decision threshold, making the system require "more time evidence" before committing to an action, which manifests behaviorally as a slowing of the clock.
Bayesian Integration
Finally, the brain is a Bayesian machine. It does not trust its internal clock blindly; it integrates the current measurement with prior knowledge (memory of distribution of intervals). If the current clock reading is noisy (e.g., due to low attention or serotonin depletion), the brain relies more heavily on the "prior"—the average interval duration. This "central tendency effect" pulls estimates toward the mean. Dopamine signaling of prediction errors (RPE) essentially updates the "posterior" distribution, constantly refining the brain's internal model of temporal statistics.
Excerpt from: Unveiling Temporal Dynamics Probing Serotonin and Dopamine Effects on Time Cell Function Through Integrated Approaches by Peter De Ceuster
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