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How Neurons Tick

von Kerstin Göpfrich (21.07.2011)

Time is relative!

Clocks seem to make the concept of time tangible. Since Einstein, however, time is no longer what the clock indicates. This finding is known to be relevant at high energies but has little influence when it comes to the range of velocities we are concerned with in our everyday life. Still, there is a dimension of the relativity of time we do experience every day when minutes seem to last for hours and hours just pass by in a flash.

But why does the apparent duration of a time interval change? Why don't we perceive time as an absolute value? How is time perception achieved in our brain? Here, a computational model of human time perception is implemented to shed light on these questions.

The stopwatch model

Most commonly, time perception is considered to be the product of a centralized internal clock that accomplishes the judgment of duration by means of a generic, universal timing mechanism. A pacemaker generates ticks at a set rate, the ticks are stored and the duration of an interval is indicated by the number of ticks. This concept of an internal clock suggests a modality independent, central cognitive mechanism, so the duration of a visual stimulus is encoded in the same way as an auditory or tactile stimulus. Recent physiological and psychophysical findings, however, provide evidence for low level, local timing mechanisms that are modality specific. For instance, there is strong evidence that magnocellular neurons in the lateral geniculate nucleus are part of the time pathway.

One reason for this assumption is that cortically invisible flicker produces duration compression in normal subjects, but not in dyslexics for whom a magnocellular impairment has been proposed (Johnston et al., 2008).

A content-dependent stopwatch model

Since these findings contradict the idea of a central internal clock, the stopwatch model has to be questioned. The basic idea of the new model, which was implemented in Matlab as part of this project, is to replace the free-running pacemaker with a 'predict-and-compare' circuit.

The algorithm takes in the visual input (here: a sine grating stimulus) and gives back the perceived duration of a time interval as a percentage of the actual duration.


The underlying mechanism is the following: First, the taylor series of the current visual input is used to make a prediction for some future point in time. Since magnocellular neurons are experimentally characterized as temporal differentiating functions (Hess et al., 1992 and Johnston et al., 1995) it is a fair assumption that they can contribute to a forward prediction.

This prediction is stored and continously compared to the sensory input, which is in reality provided by the parvocellular neurons. When the cross-correlation peaks, the clock ticks, the tick is accumulated, and the prediction is reset. At the end of the time interval the duration is read from the number of ticks stored in the accumulator.

Time distortions

Changes in the sensory input such as contrast adaption lead to changes in the filter characteristics of magnocellular cells, while parvocellular neurons remain unaffected. Often the magnocellular response is shortened, inducing a phase shift in the magnocellular signal compared to the parvocellular. Thus, the prediction is shifted forward in time, the cross correlation takes longer to peak, the clock ticks later and there will be less ticks accumulated at the end of the interval. This translates into duration compression.

Physiological measurements of the response of magnocellular cells suggest that the phase advance is continuous (Bernadete et al., 1999). The examination of the model revealed that there are two ways to achieve these results, either by varying the width of the filter that processes the input or by allowing fractional order derivatives in the taylor series.

Model outputs

Varying the model parameters led to the conclusion that the maximum duration compression lies at around 75 percent of the actual duration, which is in accordance with psychophysical observations. To be able to give an exact percentage one has to collect further physiological details on the functionality of magnocelluar neurons, in particular on the amount of forward prediction, since this parameter has a strong effect on the perceived duration. The figure shows the perceived duration as a percentage of the actual duration as a function of the amount of forward prediction and the width of the filter. When keeping the width constant and therefore varying the order of the derivative, the output looks very similar.


Both variations of the model have been applied equally successful to the physiological data from Bernadete but also to psychophysical measurements. Since varying the filter width triggers a change in amplitude of the response function that is not observed in the experiments, fractional derivatives may be regarded as the more promising approach. Still, physiological research has to indicate which of the two approaches is closer to reality.


The content-dependent stopwatch model can't and doesn't intend to explain all aspects of duration perception since encoding duration requires individuation. It can, however, predict the outcomes of expensive and time consuming psychophysical and physiological investigations and thereby help to optimize the experimental design. It can also help to pose the right questions for physiologists to answer, which may lead to groundbreaking progress in our understanding of "how neurons tick".


Kerstin Göpfrich
Kerstin Göpfrich
* 1990, Regensburg

  • from October 2011
  • Year abroad at the University of Cambridge
  • Spring 2011
  • Research visit at the University College London, under the supervision of Allan Johnston
  • 2009-today
  • Bachelor studies in Physics („Physik mit integriertem Doktorandenkolleg“) in Erlangen
  • 2008-today
  • Bachelor studies in Moleculare Medicine in Erlangen