Neurobiology of Interval Timing (Advances in Experimental Medicine and Biology, Volume 829)
Obviously, the implementation of our synaptic-learning algorithm was beneficial to our time-learning model. After several training processes, the synaptic weights will stabilize within a certain range. The duration from a firing rate of 0 to the firing-rate peak of the relative-timing cell was our target duration.
It is reasonable that there was a delay between the activation time of the motor cell and the time at which either the external stimulus appeared or the firing rate of relative cells reached threshold. Discharge-rate curves of all neuronal types for the ms experiment in an SCT time interval with our model. In the absolute-timing cell diagram, there are five firing rate curves of the pyramidal neurons in five absolute-timing groups.
Due to the stimulus signal, the peak firing rate of the relative-timing cell in the synchronous phase that is lower than that in the continuous phase. The discharge rate of the swing cell represents a cyclical change from down to up. The motor cell was activated either after the external synchronization signals appeared or the firing rate of the relative cells reached the threshold.
In our circuit, the relative-timing cell is considered to be the key to indicating the desired interval. The periodicity exhibited by each of the other neuronal groups is driven by the relative-timing cells. The discharge diagram of the relative-timing cells during several training sessions is shown in Figure 8. As the number of training sessions increase, the peak of the relative timing cells gets closer to the desired tap moment red-dashed line. Figure 9 is a plot of the times the model learned. In the figure, the points of the continuous phase of each training session have been fitted with a straight line.
It can be observed that our model's ability to learn the interval duration improved. Firing rate diagram after smoothing of relative-timing cells during several training sessions. Here the interval length is ms. The green-dashed lines represent the occurrence of external synchronization signals and the red-dashed lines indicate the desired tapping time points in the continuous phase.
As mentioned above, four types of cells related to time processing have been described previously Merchant et al. These four types of neurons also exist in the neural circuits we designed. We compared them with the electrophysiological measurements of the firing patterns of neurons as shown in Figure It is obvious that the neurons in our neural circuits exhibit periodicity and produce discharge curves similar to those observed in physiological experiments. In the left column of Figure 10A , the curves represent the firing rate of five absolute-timing groups which increase with different climbing rates for each color and span different time intervals.
Similar to the right column of Figure 10B , the time-accumulator cells we designed increased with rising at the same climbing rates as their electrophysiological counterparts, although the peaks differed for different time intervals. In order to be consistent with the discharge rate diagram of relative-timing cells in the reference, the figure in the left column of Figure 10C was plotted in the same form.
It can be seen that our relative-timing cells exhibited the same features as those in the discharge rate diagram. Figure 10D shows the firing rates of the swing cells in our model and those of the electrophysiological experiment. Although there are some differences in the curves of the two graphs of Figure 10D , our swing cells retained the characteristics of the bio-cell discharge rate. One period of the neurons we designed in the left column of Figure 10D can represent the target-time interval; the amplitude of the curve increases as the target interval duration increases.
We believe that the reason for the difference between the curves of our experimental results and those of electrophysiological experiments has to do with the fact that our results were somewhat smoothed and also that the time-window selection used to calculate the discharge rate of neurons in our model differed from that used in the electrophysiological experiments. Therefore, we consider that the differences observed in the curves of Figure 10D are acceptable. Comparison of the firing rates of all of the neurons in our model with results from electrophysiological measurements Merchant et al.
The left column is the discharge curve smoothed of the neurons in our model. The right column shows the discharge curves for all types of neurons from electrophysiological experiments. A—D respectively, illustrate the results for absolute-timing cells, time-accumulator cells, relative-timing cells, and swing cells The right column of the figure is modified from Merchant et al. The flow of our models which interprets the architecture shown in Figure 6. Finally, we tested our model to check whether it satisfies an additional biological property called the scalar property Gibbon et al.
Figure 11 shows that repeated the experiment eight times and recorded the mean of the learned duration in the ms experiment, ms experiment, and ms experiment receptively.
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According to the figure, the scalar property was followed by our model, which further confirms the biological interpretability of our work. The relationship between temporal variability and the produced duration in our model. In this study, in order to explore a possible time-processing mechanism in the human brain, we examined the time processing behind the electrophysiological phenomena observed in the SCT experiment Merchant et al.
This neural circuit was successful in determining time intervals in SCT experiments and in expressing the time intervals learned, indicating that our proposed method is reasonable and effective. Although computational simulation results— which are often more idealized— tend to differ from those of electrophysiological experiments, our simulation experiments and physiological test results were completely consistent with those of electrophysiological experiments.
This suggests that the circuit we designed is similar to the endogenous circuit of the macaque brain in terms of achieving this particular timing and periodicity operation.
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In neurobiology, the cerebral cortex can be divided into different regions according to different functions. The hierarchical structure of each brain region is essentially the same, and it is composed of six layers of neurons: molecular layer, external granular layer, external pyramidal layer, internal granular layer, internal pyramidal layer, and multiform layer Le Be', These six layers of neurons are arranged vertically in each brain region.
According to previous literature Merchant et al.
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Additionally, there are many time-related cells in the MPC. We believe that the neurons in the neural circuit we designed may also be distributed in the six layers of the MPC Figure The distribution hypothesis of our neuron-circuit model. We hypothesize that the input cells used as the cue cells should reside in the superficial layers which receive the stimuli from the outside environment.
Additionally, the motor cells used as the output cell are suitable for layer V, where the cells transmit out signals for movement.
Finally, layer III is always used to integrate the information, so the four kinds of ramp cells should reside in layer III. The most significant difference between our model and previous simulations is that our model is more biologically interpretable. And Recreating the discharge rate curves observed and scalar property in electrophysiology is another advantage of our model compared with pacemaker accumulator models Treisman, and state dependent network models Buonomano and Maass, The downside of our model is that it can only learn very precise interval durations.
In our model, we make use of TDDM algorithm, which is considered to be a fast and accurate time-learning mechanism for determining interval durations. Although humans can learn target time, there must exist some biases between the time learned and target time. Hence, the high accuracy which is the advantage of TDDM algorithm cannot be interpreted biologically. A certain degree of biases are necessarily presented in human experiments. Knudsen et al. Their work provided us more information to improve our model in the future. In addition, we will improve our learning-mechanism algorithm to satisfy additional biological properties and be flexible in more temporal-processing experiments.
And now this work is based on the property called ramp activity, but future studies will explore other properties as well. We believe that as more and more time-related biological properties are adopted, our model will become closer to endogenous biological processing mechanisms. HW carried out the computational neuroscience model and neural circuit design studies, experiment design, and writing the paper.
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This may be because the snippet appears in a figure legend, contains special characters or spans different sections of the article. Front Comput Neurosci. Published online Jun PMID: Received Dec 16; Accepted Jun The use, distribution or reproduction in other forums is permitted, provided the original author s and the copyright owner s are credited and that the original publication in this journal is cited, in accordance with accepted academic practice.
No use, distribution or reproduction is permitted which does not comply with these terms. This article has been cited by other articles in PMC. Abstract Time is a continuous, homogeneous, one-way, and independent signal that cannot be modified by human will. Keywords: time-related neuron, time-processing circuit, spiking-neuron, synaptic learning, ramp activity, SCT. Introduction When we use visual cues to observe the environment, we need to grasp both the time interval and the sequence of various events.
Synchronization-Continuation Tapping Task In this study, the model we employed was based on experiments on the millisecond scale. Open in a separate window. Figure 1. Ramp Activity One of the most important tasks of the brain is to anticipate upcoming events in order to prepare for behavior, anticipate reactions, and plan.
Structure of This Paper The remainder of this paper details our research as follows: related works are presented in section Related Work.
A Temporal Signal-Processing Circuit Based on Spiking Neuron and Synaptic Learning
Related Work There are many computational models for time-dependent signal processing, including pacemaker accumulator models Treisman, , state dependent network models Buonomano and Maass, , long short-term memory models LSTM Rivest et al. A Spiking-Neuron Circuit for Temporal Signal-Processing Neuron Model In this paper, a simple spiking neuron model known as the Izhikevich neuron model was used to simplify the Hodgkin—Huxley HH model into a 2-D system with sufficient biological plausibility and high computational efficiency Izhikevich, Figure 2.
Figure 3. Neural-Circuit Model Our neural circuit model was designed based on previous study Merchant et al.
Relative-timing cells interact with absolute-timing cells and their activity becomes locked at some point, resulting in a balanced loop mechanism for executing motor sequences with tight time structures. Neuronal activity of an absolute-timing cell exhibits an increase in its up-down profile of activation across different intervals. And they found that the duration of the up-down cycle of activity in absolute timing cells is associated with subjective time. The discharge diagram of a time-accumulator cell is similar to that of absolute-timing cells which represents the passage of time since the previous movement.
And in time-accumulator cells, there is an additional increase in peak magnitude as a function of elapsed time. Thus, their slopes are similar across different target time intervals. As the target interval increases, the discharge period of swing cells increases. In addition the firing rates of swing cells always decrease and then increase within a target interval. We consider that the effect of swing cells may be to represent the interval length. Figure 4. Figure 5. The microcircuit for swing cells which represent time interval.