Mathematical microscope sheds light on efficient memory formation even during sleep

University of California - Los Angeles Health SciencesMay 8 2024

UCLA Health researchers have discovered a mechanism that creates memories while reducing metabolic cost, even during sleep. This efficient memory occurs in a part of the brain that is crucial for learning and memory, and where Alzheimer's disease begins. 

The discovery is published in the journal Nature Communications. 

Does this sound familiar: You go to the kitchen to fetch something, but when you get there, you forget what you wanted. This is your working memory failing. Working memory is defined as remembering some information for a short period while you go about doing other things. We use working memory virtually all the time. Alzheimer's and dementia patients have working memory deficits and it also shows up in mild cognitive impairment (MCI). Hence, considerable effort has been devoted to understand the mechanisms by which the vast networks of neurons in the brain create working memory. 

During working memory tasks, the outermost layer of the brain, known as the neocortex, sends sensory information to deeper regions of the brain, including a central region called the entorhinal cortex, which is crucial for forming memories. Neurons in the entorhinal cortex show a complex array of responses, which have puzzled scientists for a long time and resulted in the 2014 Nobel Prize in medicine, yet the mechanisms governing this complexity are unknown. The entorhinal cortex is where Alzheimer's disease begins forming. 

It's therefore critical to understand what kind of magic happens in the cortico-entorhinal network, when the neocortex speaks to the entorhinal cortex which turns it into working memory. It could provide an early diagnostic of Alzheimer's disease and related dementia, and mild cognitive impairment."

Mayank Mehta, corresponding author, neurophysicist and head of the W. M. Keck Center for Neurophysics and the Center for Physics of Life at UCLA

To crack this problem, Mehta and his coauthors devised a novel approach: a "mathematical microscope." 

In the world of physics, mathematical models are commonly used, from Kepler to Newton and Einstein, to reveal amazing things we have never seen or even imagined, such as the inner workings of subatomic particles and the inside of a black hole. Mathematical models are used in brain sciences too, but their predictions are not taken as seriously as in physics. The reason is that in physics, predictions of mathematical theories are tested quantitatively, not just qualitatively. 

Such quantitatively precise experimental tests of mathematical theories are commonly believed to be unfeasible in biology because the brain is vastly more complex than the physical world. Mathematical theories in physics are very simple, involving very few free parameters and hence precise experimental tests. In contrast, the brain has billions of neurons and trillions of connections, a mathematical nightmare, let alone a highly precise microscope. 

"To tackle this seemingly impossible challenge of devising a simple theory that can still explain the experimental of data of memory dynamics in vivo data with high precision, we hypothesized that cortico-entorhinal dialog, and memory magic, will occur even when the subjects are sleeping, or anesthetized," said Dr. Krishna Choudhary, the lead author of the study. "Just like a car behaves like a car when it's idling or going at 70 mph." 

UCLA researchers then made another large assumption: the dynamics of the entire cortex and the entorhinal cortex during sleep or anesthesia can be captured by just two neurons. These assumptions reduced the problem of billions of neurons' interactions to just two only free variables – the strength of input from the neocortex to entorhinal cortex and the strength of recurrent connections within the entorhinal cortex. While this makes the problem mathematically tractable, it raises the obvious question – is it true? 

"If we test our theory quantitatively on data in vivo, then these are just interesting mathematical games, not a solid understanding of memory-making magic," said Mehta. 

The crucial experimental tests of this theory required sophisticated experiments by Dr. Thomas Hahn, a coauthor who is now professor at Basel University and a clinical psychologist. 

"The entorhinal cortex is a complicated circuit. To really test the theory we needed experimental techniques that can not only measure the neural activity with high precision, but also determine the precise anatomical identity of the neuron," said Hahn. 

Hahn and Dr. Sven Berberich, also a coauthor, measured the membrane potential of identified neurons from the entorhinal cortex in vivo, using whole cell patch clamp technique and then used anatomical techniques to identify the neuron. Simultaneously they measured the activity of the parietal cortex, a part of neocortex that sends inputs to the entorhinal cortex. 

"A mathematical theory and sophisticated in vivo data are necessary and cool, but we had to tackle one more challenge – how does one map this simple theory onto complex neural data?" said Mehta. 

"This required a protracted period of development, to generate a 'mathematical microscope' that can directly reveal the inner workings of neurons as they make memory," said Choudhary. "As far as we know, this has not been done before." 

The authors observed that like an ocean wave forming and then crashing on to a shoreline, the signals from the neocortex oscillate between on and off states in intervals while a person or animal sleeps. Meanwhile, the entorhinal cortex acted like a swimmer in the water who can move up when the wave forms and then down when it recedes. The data showed this and the model captured this as well. But using this simple match the model then took a life of its own and discovered a new type of memory state known as spontaneous persistent inactivity, said Mehta. 

"It's as if a wave comes in and the entorhinal cortex said, 'There is no wave! I'm going to remember that recently there was no wave so I am going to ignore this current wave and not respond at all'. This is persistent inactivity" Mehta said. "Alternately, persistent activity occurs when the cortical wave disappears but the entorhinal neurons remember that there was a wave very recently, and continue rolling forward." 

While many theories of working memory had shown the presence of persistent activity, which the authors found, the persistent inactivity was something that the model predicted and had never been seen before. 

"The cool part about persistent inactivity is that it takes virtually no energy, unlike persistent activity, which takes a lot of energy", said Mehta, "even better, the combination of persistent activity and inactivity more than doubles the memory capacity while cutting down the metabolic energy cost by half." 

"All this sounded too good to be true, so we really pushed our mathematical microscope to the limit, into a regime where it was not designed to work," said Dr. Choudhary. "If the microscope was right, it would continue working perfectly even in unusual situations." 

"The math-microscope made a dozen predictions, not just about entorhinal but many other brain regions too. To our complete surprise, the mathematical microscope worked every time," Mehta continued. "Such near perfect match between the predictions of a mathematical theory and experiments is unprecedented in neuroscience. 

"This mathematical model that is perfectly matched with experiments is a new microscope," Mehta continued. "It reveals something that no existing microscope could see without it. No matter how many neurons you have imaged, it would not have revealed any of this. 

"In fact, metabolic shortcomings are a common feature of many memory disorders," said Mehta. Mehta's laboratory is now following up on this work to understand how complex working memory is formed, and what goes wrong in the entorhinal cortex during Alzheimer's disease, dementia and other memory disorders."