Marshall G. Hussain Shuler

Learning reward timing in cortex through reward dependent expression of synaptic plasticity

The ability to represent time is an essential component of cognition but its neural basis is unknown. Although extensively studied both behaviorally and electrophysiologically, a general theoretical framework describing the elementary neural mechanisms used by the brain to learn temporal representations is lacking. It is commonly believed that the underlying cellular mechanisms reside in high order cortical regions but recent studies show sustained neural activity in primary sensory cortices that can represent the timing of expected reward. Here, we show that local cortical networks can learn temporal representations through a simple framework predicated on reward dependent expression of synaptic plasticity. We assert that temporal representations are stored in the lateral synaptic connections between neurons and demonstrate that reward-modulated plasticity is sufficient to learn these representations. We implement our model numerically to explain reward-time learning in the primary visual cortex (V1), demonstrate experimental support, and suggest additional experimentally verifiable predictions.

Optogenetic dissection of the basal forebrain neuromodulatory control of cortical activation, plasticity, and cognition

The basal forebrain (BF) houses major ascending projections to the entire neocortex that have long been implicated in arousal, learning, and attention. The disruption of the BF has been linked with major neurological disorders, such as coma and Alzheimers disease, as well as in normal cognitive aging. Although it is best known for its cholinergic neurons, the BF is in fact an anatomically and neurochemically complex structure. Recent studies using transgenic mouse lines to target specific BF cell types have led to a renaissance in the study of the BF and are beginning to yield new insights about cell-type-specific circuit mechanisms during behavior. These approaches enable us to determine the behavioral conditions under which cholinergic and noncholinergic BF neurons are activated and how they control cortical processing to influence behavior. Here we discuss recent advances that have expanded our knowledge about this poorly understood brain region and laid the foundation for future cell-type-specific manipulations to modulate arousal, attention, and cortical plasticity in neurological disorders. SIGNIFICANCE STATEMENT Although the basal forebrain is best known for, and often equated with, acetylcholine-containing neurons that provide most of the cholinergic innervation of the neocortex, it is in fact an anatomically and neurochemically complex structure. Recent studies using transgenic mouse lines to target specific cell types in the basal forebrain have led to a renaissance in this field and are beginning to dissect circuit mechanisms in the basal forebrain during behavior. This review discusses recent advances in the roles of basal forebrain cholinergic and noncholinergic neurons in cognition via their dynamic modulation of cortical activity.

Visually Cued Action Timing in the Primary Visual Cortex

Most behaviors are generated in three steps: sensing the external world, processing that information to instruct decision-making, and producing a motor action. Sensory areas, especially primary sensory cortices, have long been held to be involved only in the first step of this sequence. Here, we develop a visually cued interval timing task that requires rats to decide when to perform an action following a brief visual stimulus. Using single-unit recordings and optogenetics in this task, we show that activity generated by the primary visual cortex (V1) embodies the target interval and may instruct the decision to time the action on a trial-by-trial basis. A spiking neuronal model of local recurrent connections in V1 produces neural responses that predict and drive the timing of future actions, rationalizing our observations. Our data demonstrate that the primary visual cortex may contribute to the instruction of visually cued timed actions.

A general theory of intertemporal decision-making and the perception of time

Animals and humans make decisions based on their expected outcomes. Since relevant outcomes are often delayed, perceiving delays and choosing between earlier vs. later rewards (intertemporal decision-making) is an essential component of animal behavior. The myriad observations made in experiments studying intertemporal decision-making and time perception have not yet been rationalized within a single theory. Here we present a theory—Training-Integrated Maximized Estimation of Reinforcement Rate (TIMERR)—that explains a wide variety of behavioral observations made in intertemporal decision-making and the perception of time. Our theory postulates that animals make intertemporal choices to optimize expected reward rates over a limited temporal window which includes a past integration interval—over which experienced reward rate is estimated—as well as the expected delay to future reward. Using this theory, we derive mathematical expressions for both the subjective value of a delayed reward and the subjective representation of the delay. A unique contribution of our work is in finding that the past integration interval directly determines the steepness of temporal discounting and the non-linearity of time perception. In so doing, our theory provides a single framework to understand both intertemporal decision-making and time perception.

Rationalizing Decision-Making: Understanding the Cost and Perception of Time

Humans, as with other animals, decide between courses of action based on the evaluation of the relative worth of expected outcomes. How outcome magnitude interacts with temporal delay, however, has yet eluded a principled understanding that reconciles the breadth of well-established behaviors in intertemporal decision-making. Here, we review the history of this endeavor to rationalize decision-making regarding the domain of time, highlighting extant theories, their limitations, and recent experimental and theoretical advances. These new advances recast long presumed deficiencies in observed decision-making behavior, not as flaws, but rather as signs of optimal decision-making under experiential constraints. This new conception naturally unites the fields of intertemporal decision-making and time perception, which have long been recognized to be interconnected but not yet unified in a formal framework.

Theta Oscillations in Visual Cortex Emerge with Experience to Convey Expected Reward Time and Experienced Reward Rate

The primary visual cortex (V1) is widely regarded as faithfully conveying the physical properties of visual stimuli. Thus, experience-induced changes in V1 are often interpreted as improving visual perception (i.e., perceptual learning). Here we describe how, with experience, cue-evoked oscillations emerge in V1 to convey expected reward time as well as to relate experienced reward rate. We show, in chronic multisite local field potential recordings from rat V1, that repeated presentation of visual cues induces the emergence of visually evoked oscillatory activity. Early in training, the visually evoked oscillations relate to the physical parameters of the stimuli. However, with training, the oscillations evolve to relate the time in which those stimuli foretell expected reward. Moreover, the oscillation prevalence reflects the reward rate recently experienced by the animal. Thus, training induces experience-dependent changes in V1 activity that relate to what those stimuli have come to signify behaviorally: when to expect future reward and at what rate.

A temporal basis for Weber's law in value perception

Webers law—the observation that the ability to perceive changes in magnitudes of stimuli is proportional to the magnitude—is a widely observed psychophysical phenomenon. It is also believed to underlie the perception of reward magnitudes and the passage of time. Since many ecological theories state that animals attempt to maximize reward rates, errors in the perception of reward magnitudes and delays must affect decision-making. Using an ecological theory of decision-making (TIMERR), we analyze the effect of multiple sources of noise (sensory noise, time estimation noise, and integration noise) on reward magnitude and subjective value perception. We show that the precision of reward magnitude perception is correlated with the precision of time perception and that Webers law in time estimation can lead to Webers law in value perception. The strength of this correlation is predicted to depend on the reward history of the animal. Subsequently, we show that sensory integration noise (either alone or in combination with time estimation noise) also leads to Webers law in reward magnitude perception in an accumulator model, if it has balanced Poisson feedback. We then demonstrate that the noise in subjective value of a delayed reward, due to the combined effect of noise in both the perception of reward magnitude and delay, also abides by Webers law. Thus, in our theory we prove analytically that the perception of reward magnitude, time, and subjective value change all approximately obey Webers law.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework.

Significance Understanding the movement patterns of wild animals is a fundamental question in ecology with implications for wildlife conservation. It has recently been hypothesized that random search patterns known as Lévy walks are optimal and underlie the observed power law movement patterns of wild foragers. However, as Lévy walk models assume that foragers do not learn from experience, they may not apply generally to cognitive animals. Here, we present a decision-theoretic framework wherein animals attempting to optimally learn from their environments will show near power law-distributed path lengths due to temporal discounting. We then provide experimental support for this framework in human exploration in a controlled laboratory setting and in animals foraging in the wild. Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

A Simple Network Architecture Accounts for Diverse Reward Time Responses in Primary Visual Cortex

Many actions performed by animals and humans depend on an ability to learn, estimate, and produce temporal intervals of behavioral relevance. Exemplifying such learning of cued expectancies is the observation of reward-timing activity in the primary visual cortex (V1) of rodents, wherein neural responses to visual cues come to predict the time of future reward as behaviorally experienced in the past. These reward-timing responses exhibit significant heterogeneity in at least three qualitatively distinct classes: sustained increase or sustained decrease in firing rate until the time of expected reward, and a class of cells that reach a peak in firing at the expected delay. We elaborate upon our existing model by including inhibitory and excitatory units while imposing simple connectivity rules to demonstrate what role these inhibitory elements and the simple architectures play in sculpting the response dynamics of the network. We find that simply adding inhibition is not sufficient for obtaining the different distinct response classes, and that a broad distribution of inhibitory projections is necessary for obtaining peak-type responses. Furthermore, although changes in connection strength that modulate the effects of inhibition onto excitatory units have a strong impact on the firing rate profile of these peaked responses, the network exhibits robustness in its overall ability to predict the expected time of reward. Finally, we demonstrate how the magnitude of expected reward can be encoded at the expected delay in the network and how peaked responses express this reward expectancy. SIGNIFICANCE STATEMENT Heterogeneity in single-neuron responses is a common feature of neuronal systems, although sometimes, in theoretical approaches, it is treated as a nuisance and seldom considered as conveying a different aspect of a signal. In this study, we focus on the heterogeneous responses in the primary visual cortex of rodents trained with a predictable delayed reward time. We describe under what conditions this heterogeneity can arise by self-organization, and what information it can convey. This study, while focusing on a specific system, provides insight onto how heterogeneity can arise in general while also shedding light onto mechanisms of reinforcement learning using realistic biological assumptions.

Analytical calculation of errors in time and value perception due to a subjective time accumulator: A mechanistic model and the generation of weber's law

It has been previously shown (Namboodiri, Mihalas, Marton, & Hussain Shuler, 2014) that an evolutionary theory of decision making and time perception is capable of explaining numerous behavioral observations regarding how humans and animals decide between differently delayed rewards of differing magnitudes and how they perceive time. An implementation of this theory using a stochastic drift-diffusion accumulator model (Namboodiri, Mihalas, & Hussain Shuler, 2014a) showed that errors in time perception and decision making approximately obey Weber’s law for a range of parameters. However, prior calculations did not have a clear mechanistic underpinning. Further, these calculations were only approximate, with the range of parameters being limited. In this letter, we provide a full analytical treatment of such an accumulator model, along with a mechanistic implementation, to calculate the expression of these errors for the entirety of the parameter space. In our mechanistic model, Weber’s law results from synaptic facilitation and depression within the feedback synapses of the accumulator. Our theory also makes the prediction that the steepness of temporal discounting can be affected by requiring the precise timing of temporal intervals. Thus, by presenting exact quantitative calculations, this work provides falsifiable predictions for future experimental testing.