Fuat Balcı

A Model of Interval Timing by Neural Integration

We show that simple assumptions about neural processing lead to a model of interval timing as a temporal integration process, in which a noisy firing-rate representation of time rises linearly on average toward a response threshold over the course of an interval. Our assumptions include: that neural spike trains are approximately independent Poisson processes, that correlations among them can be largely cancelled by balancing excitation and inhibition, that neural populations can act as integrators, and that the objective of timed behavior is maximal accuracy and minimal variance. The model accounts for a variety of physiological and behavioral findings in rodents, monkeys, and humans, including ramping firing rates between the onset of reward-predicting cues and the receipt of delayed rewards, and universally scale-invariant response time distributions in interval timing tasks. It furthermore makes specific, well-supported predictions about the skewness of these distributions, a feature of timing data that is usually ignored. The model also incorporates a rapid (potentially one-shot) duration-learning procedure. Human behavioral data support the learning rules predictions regarding learning speed in sequences of timed responses. These results suggest that simple, integration-based models should play as prominent a role in interval timing theory as they do in theories of perceptual decision making, and that a common neural mechanism may underlie both types of behavior.

Risk assessment in man and mouse

Human and mouse subjects tried to anticipate at which of 2 locations a reward would appear. On a randomly scheduled fraction of the trials, it appeared with a short latency at one location; on the complementary fraction, it appeared after a longer latency at the other location. Subjects of both species accurately assessed the exogenous uncertainty (the probability of a short versus a long trial) and the endogenous uncertainty (from the scalar variability in their estimates of an elapsed duration) to compute the optimal target latency for a switch from the short- to the long-latency location. The optimal latency was arrived at so rapidly that there was no reliably discernible improvement over trials. Under these nonverbal conditions, humans and mice accurately assess risks and behave nearly optimally. That this capacity is well-developed in the mouse opens up the possibility of a genetic approach to the neurobiological mechanisms underlying risk assessment.

Acquisition of decision making criteria: reward rate ultimately beats accuracy

Speed–accuracy trade-offs strongly influence the rate of reward that can be earned in many decision-making tasks. Previous reports suggest that human participants often adopt suboptimal speed–accuracy trade-offs in single session, two-alternative forced-choice tasks. We investigated whether humans acquired optimal speed–accuracy trade-offs when extensively trained with multiple signal qualities. When performance was characterized in terms of decision time and accuracy, our participants eventually performed nearly optimally in the case of higher signal qualities. Rather than adopting decision criteria that were individually optimal for each signal quality, participants adopted a single threshold that was nearly optimal for most signal qualities. However, setting a single threshold for different coherence conditions resulted in only negligible decrements in the maximum possible reward rate. Finally, we tested two hypotheses regarding the possible sources of suboptimal performance: (1) favoring accuracy over reward rate and (2) misestimating the reward rate due to timing uncertainty. Our findings provide support for both hypotheses, but also for the hypothesis that participants can learn to approach optimality. We find specifically that an accuracy bias dominates early performance, but diminishes greatly with practice. The residual discrepancy between optimal and observed performance can be explained by an adaptive response to uncertainty in time estimation.

Chronic administration of infliximab (TNF-α inhibitor) decreases depression and anxiety-like behaviour in rat model of chronic mild stress.

Pro‐inflammatory cytokines have been proposed to be associated with the pathogenesis of depression. Consistent with this notion, several clinical observations have suggested the antidepressant efficacy of TNF‐α inhibitors in patients with chronic inflammatory diseases. In this study, we evaluated the antidepressant and anxiolytic effects of chronic TNF‐α inhibitor (infliximab, 5 mg/kg, i.p., weekly) administration in the chronic mild stress (CMS) model of depression. Rats were divided into three groups: saline‐control (no stress), saline‐CMS, and infliximab‐CMS. Rats in the latter two groups were exposed to CMS for 8 weeks. Saline (former two groups) or infliximab was injected weekly during this period. After CMS, total locomotor activity, anxiety‐like behaviour and depression‐like behaviours were evaluated using automated locomotor activity cage, elevated plus maze (EPM), and sucrose preference (SPT) and forced swimming (FS) tests, respectively. As expected, the saline‐CMS group exhibited higher depression‐like behaviours in FS and SPT tests compared with the saline‐control group. There were no differences between these two groups in terms of the anxiety‐like behaviour or total locomotor activity. Infliximab reduced the depression‐like behaviour of CMS rats compared with saline‐CMS group, and anxiety‐like behaviour of CMS rats compared with saline‐CMS and saline‐control groups. Our findings suggest that chronic and systemic TNF‐α inhibition reduced depression and anxiety‐like behaviour in the CMS model of depression in rats.

Timing Deficits in Aging and Neuropathology

The capacity to capture the temporal information embedded in biologically relevant events is a necessary and ubiquitous ability of higher organisms. The cognitive apparatus that supports timing is integrally entwined with those supporting other cognitive processes including memory and attention. In this chapter, we argue that timing deficits consistently occur with aging and in specific neurodegenerative disorders (i.e., Parkinson’s disorder and Huntington disease), and might depend on and reflect attentional deficits that are also characteristic of normal aging and in these clinical populations. We review the impairments in temporal information processing seen in the elderly and in neural disease, and evaluate them in relation with the structural and neurochemical brain markers. Given the good correspondence between the psychophysical properties of interval timing across nonhuman and humans, we further argue that interval timing might serve as a quantitative model for cognitive aging that offers promise in the translation from preclinical to clinical studies.

Acquisition of peak responding: What is learned?

We investigated how the common measures of timing performance behaved in the course of training on the peak procedure in C3H mice. Following fixed interval (FI) pre-training, mice received 16 days of training in the peak procedure. The peak time and spread were derived from the average response rates while the start and stop times and their relative variability were derived from a single-trial analysis. Temporal precision (response spread) appeared to improve in the course of training. This apparent improvement in precision was, however, an averaging artifact; it was mediated by the staggered appearance of timed stops, rather than by the delayed occurrence of start times. Trial-by-trial analysis of the stop times for individual subjects revealed that stops appeared abruptly after three to five sessions and their timing did not change as training was prolonged. Start times and the precision of start and stop times were generally stable throughout training. Our results show that subjects do not gradually learn to time their start or stop of responding. Instead, they learn the duration of the FI, with robust temporal control over the start of the response; the control over the stop of response appears abruptly later.

Motivational effects on interval timing in dopamine transporter (DAT) knockdown mice

We examined interval timing in mice that underexpress the dopamine transporter (DAT) and have chronically higher levels of extracellular dopamine (Zhuang et al., 2001). The dopaminergic system has been proposed as a neural substrate for an internal clock, with transient elevations of dopaminergic activity producing underestimation of temporal intervals. A group of DAT knockdown (KD) and littermate wild type (WT) mice were tested with a dual peak procedure. Mice obtained reinforcement by pressing one of two levers after a fixed amount of time (30 or 45 s) had elapsed since lever extension. Only one lever was available at a time, and each lever was associated with a single duration. On occasional probe trials, the DAT KD mice began responding earlier in the interval than WT mice, but showed maximal responding and terminated responding around the same time as the WT mice. Administration of raclopride (0.2, 0.6, and 1.2 mg/kg), a D2 antagonist, eliminated most of the differences between DAT KD and WT mice, suggesting that the effects of chronic DAT downregulation on interval timing were mediated by the D2 receptors. Another cohort of DAT KD mice was trained on a visual attention task, and no deficits were observed, confirming that the changes in timed behavior were not attentionally mediated. Our data are consistent with the view that tonic dopamine affects the sensitivity of an organism to external reward signals, and that this increased motivation for reward of DAT KD mice lowers the threshold for initiating responding in a timing task.

Interval timing in genetically modified mice: a simple paradigm

We describe a behavioral screen for the quantitative study of interval timing and interval memory in mice. Mice learn to switch from a short‐latency feeding station to a long‐latency station when the short latency has passed without a feeding. The psychometric function is the cumulative distribution of switch latencies. Its median measures timing accuracy and its interquartile interval measures timing precision. Next, using this behavioral paradigm, we have examined mice with a gene knockout of the receptor for gastrin‐releasing peptide that show enhanced (i.e. prolonged) freezing in fear conditioning. We have tested the hypothesis that the mutants freeze longer because they are more uncertain than wild types about when to expect the electric shock. The knockouts however show normal accuracy and precision in timing, so we have rejected this alternative hypothesis. Last, we conduct the pharmacological validation of our behavioral screen using d‐amphetamine and methamphetamine. We suggest including the analysis of interval timing and temporal memory in tests of genetically modified mice for learning and memory and argue that our paradigm allows this to be done simply and efficiently.

Optimal temporal risk assessment

Time is an essential feature of most decisions, because the reward earned from decisions frequently depends on the temporal statistics of the environment (e.g., on whether decisions must be made under deadlines). Accordingly, evolution appears to have favored a mechanism that predicts intervals in the seconds to minutes range with high accuracy on average, but significant variability from trial to trial. Importantly, the subjective sense of time that results is sufficiently imprecise that maximizing rewards in decision-making can require substantial behavioral adjustments (e.g., accumulating less evidence for a decision in order to beat a deadline). Reward maximization in many daily decisions therefore requires optimal temporal risk assessment. Here, we review the temporal decision-making literature, conduct secondary analyses of relevant published datasets, and analyze the results of a new experiment. The paper is organized in three parts. In the first part, we review literature and analyze existing data suggesting that animals take account of their inherent behavioral variability (their “endogenous timing uncertainty”) in temporal decision-making. In the second part, we review literature that quantitatively demonstrates nearly optimal temporal risk assessment with sub-second and supra-second intervals using perceptual tasks (with humans and mice) and motor timing tasks (with humans). We supplement this section with original research that tested human and rat performance on a task that requires finding the optimal balance between two time-dependent quantities for reward maximization. This optimal balance in turn depends on the level of timing uncertainty. Corroborating the reviewed literature, humans and rats exhibited nearly optimal temporal risk assessment in this task. In the third section, we discuss the role of timing uncertainty in reward maximization in two-choice perceptual decision-making tasks and review literature that implicates timing uncertainty as an important factor in performance quality. Together, these studies strongly support the hypothesis that animals take normative account of their endogenous timing uncertainty. By incorporating the psychophysics of interval timing into the study of reward maximization, our approach bridges empirical and theoretical gaps between the interval timing and decision-making literatures.

Cross-domain transfer of quantitative discriminations. Is it all a matter of proportion?

Meck and Church (1983) estimated a 5:1 scale factor relating the mental magnitudes representing number to the mental magnitudes representing duration. We repeated their experiment with human subjects. We obtained transfer regardless of the objective scaling between the ranges; a 5:1 scaling for number versus duration (measured in seconds) was not necessary. We obtained transfer even when the proportions between the endpoints of the number range were different. We conclude that, at least in human subjects, transfer from a discrimination based on continuous quantity (duration) to a discrimination based on discrete quantity (number) is mediated by the cross-domain comparability of withindomain proportions. The results of our second and third experiments also suggest that the subjects compare a probe with a criterion determined by the range of stimuli tested rather than by trial-specific referents, in accordance with the pseudologistic model of Killeen, Fetterman, and Bizo (1997).