It began about a decade ago at Syracuse University, with a set of equations scrawled on a blackboard. Marc Howard, a cognitive neuroscientist now at Boston University, and Karthik Shankar, who was then one of his postdoctoral students, wanted to figure out a mathematical model of time processing: a neurologically computable function for representing the past, like a mental canvas onto which the brain could paint memories and perceptions. “Think about how the retina acts as a display that provides all kinds of visual information,” Howard said. “That’s what time is, for memory. And we want our theory to explain how that display works.”
But it’s fairly straightforward to represent a tableau of visual information, like light intensity or brightness, as functions of certain variables, like wavelength, because dedicated receptors in our eyes directly measure those qualities in what we see. The brain has no such receptors for time. “Color or shape perception, that’s much more obvious,” said Masamichi Hayashi, a cognitive neuroscientist at Osaka University in Japan. “But time is such an elusive property.” To encode that, the brain has to do something less direct.
Pinpointing what that looked like at the level of neurons became Howard and Shankar’s goal. Their only hunch going into the project, Howard said, was his “aesthetic sense that there should be a small number of simple, beautiful rules.”
They came up with equations to describe how the brain might in theory encode time indirectly. In their scheme, as sensory neurons fire in response to an unfolding event, the brain maps the temporal component of that activity to some intermediate representation of the experience — a Laplace transform, in mathematical terms. That representation allows the brain to preserve information about the event as a function of some variable it can encode rather than as a function of time (which it can’t). The brain can then map the intermediate representation back into other activity for a temporal experience — an inverse Laplace transform — to reconstruct a compressed record of what happened when.
Just a few months after Howard and Shankar started to flesh out their theory, other scientists independently uncovered neurons, dubbed “time cells,” that were “as close as we can possibly get to having that explicit record of the past,” Howard said. These cells were each tuned to certain points in a span of time, with some firing, say, one second after a stimulus and others after five seconds, essentially bridging time gaps between experiences. Scientists could look at the cells’ activity and determine when a stimulus had been presented, based on which cells had fired. This was the inverse-Laplace-transform part of the researchers’ framework, the approximation of the function of past time. “I thought, oh my god, this stuff on the blackboard, this could be the real thing,” Howard said.
“It was then I knew the brain was going to cooperate,” he added.
Invigorated by empirical support for their theory, he and his colleagues have been working on a broader framework, which they hope to use to unify the brain’s wildly different types of memory, and more: If their equations are implemented by neurons, they could be used to describe not just the encoding of time but also a slew of other properties — even thought itself.
But that’s a big if. Since the discovery of time cells in 2008, the researchers had seen detailed, confirming evidence of only half of the mathematics involved. The other half — the intermediate representation of time — remained entirely theoretical.
Until last summer.
Orderings and Timestamps
In 2007, a couple of years before Howard and Shankar started tossing around ideas for their framework, Albert Tsao (now a postdoctoral researcher at Stanford University) was an undergraduate student doing an internship at the Kavli Institute for Systems Neuroscience in Norway. He spent the summer in the lab of May-Britt Moser and Edvard Moser, who had recently discovered grid cells — the neurons responsible for spatial navigation — in a brain area called the medial entorhinal cortex. Tsao wondered what its sister structure, the lateral entorhinal cortex, might be doing. Both regions provide major input to the hippocampus, which generates our “episodic” memories of experiences that occur at a particular time in a particular place. If the medial entorhinal cortex was responsible for representing the latter, Tsao reasoned, then maybe the lateral entorhinal cortex harbored a signal of time.
That’s when [Tsao] saw it: a firing pattern that, to him, looked a lot like time.
The kind of memory-linked time Tsao wanted to think about is deeply rooted in psychology. For us, time is a sequence of events, a measure of gradually changing content. That explains why we remember recent events better than ones from long ago, and why when a certain memory comes to mind, we tend to recall events that occurred around the same time. But how did that add up to an ordered temporal history, and what neural mechanism enabled it?
Tsao didn’t find anything at first. Even pinning down how to approach the problem was tricky because, technically, everything has some temporal quality to it. He examined the neural activity in the lateral entorhinal cortex of rats as they foraged for food in an enclosure, but he couldn’t make heads or tails of what the data showed. No distinctive time signal seemed to emerge.
Tsao tabled the work, returned to school and for years left the data alone. Later, as a graduate student in the Moser lab, he decided to revisit it, this time trying a statistical analysis of cortical neurons at a population level. That’s when he saw it: a firing pattern that, to him, looked a lot like time.
He, the Mosers and their colleagues set up experiments to test this connection further. In one series of trials, a rat was placed in a box, where it was free to roam and forage for food. The researchers recorded neural activity from the lateral entorhinal cortex and nearby brain regions. After a few minutes, they took the rat out of the box and allowed it to rest, then put it back in. They did this 12 times over about an hour and a half, alternating the colors of the walls (which could be black or white) between trials.
What looked like time-related neural behavior arose mainly in the lateral entorhinal cortex. The firing rates of those neurons abruptly spiked when the rat entered the box. As the seconds and then minutes passed, the activity of the neurons decreased at varying rates. That activity ramped up again at the start of the next trial, when the rat reentered the box. Meanwhile, in some cells, activity declined not only during each trial but throughout the entire experiment; in other cells, it increased throughout.