Summary: Researchers have developed a new mathematical model that helps explain how the brain forms new memories without erasing older ones.
Source: Zuckerman Institute.
New mathematical model resolves a long-standing question about memory and offers a framework to guide future studies.
Scientists at Columbia University have introduced a mathematical model that clarifies how the biological complexity of the human brain enables it to store new memories while preserving older ones. The model shows how memory fidelity can be maintained for years, decades, or even a lifetime. It provides a theoretical foundation that can guide experimental research in neuroscience and may also influence the design of neuromorphic hardware—computing systems modeled after the brain.
This work appears in Nature Neuroscience.
“The brain is constantly receiving, organizing and storing information. These processes are extremely complex, and mathematical models are essential to understand the principles that underlie memory,” said Stefano Fusi, PhD, principal investigator at Columbia’s Mortimer B. Zuckerman Mind Brain Behavior Institute, associate professor of neuroscience at Columbia University Medical Center, and the paper’s senior author. “Our model explains why the molecular and biochemical machinery involved in memory is so intricate, and how that complexity supports reliable long-term memory.”
Neuroscientists generally agree that memories are encoded in synapses, the small structures on neurons that transmit signals between cells. Early models likened synapses to simple volume knobs: adjusting the knob increased or decreased the strength of the connection between neurons, allowing memories to form. Those simple models explained why brains have such large memory capacity, but they also raised a puzzle.
“A problem with the dial-like model was the implicit assumption that synaptic strength could be adjusted indefinitely,” Dr. Fusi said. “In reality, biological systems have limits. A dial can’t turn forever.” When those biological limits were included in earlier models, the predicted memory capacity dropped dramatically.
To address this, Dr. Fusi and collaborator Larry Abbott, PhD, proposed that each synapse is not a single dial but a system of multiple interacting components. In 2005 they described how several internal variables—representing different molecular or biochemical elements—could work together to encode new memories while protecting older ones. Yet subsequent work indicated that even that multi-component model underestimated the brain’s storage capabilities.
“We realized that the different synaptic components not only operate on distinct timescales but also interact with one another,” said Marcus Benna, PhD, an associate research scientist at Columbia’s Center for Theoretical Neuroscience and lead author of the new paper. “When we included these bidirectional interactions in our model, memory capacity increased dramatically and more closely matched what we observe in living brains.”
Benna uses an analogy of interconnected beakers to describe the model. Each beaker represents a synaptic component and contains a different level of liquid. Adding or removing liquid in one beaker simulates encoding a new memory; over time the liquid flows between beakers, diffusing and stabilizing the change. This flow captures how information initially stored in fast-changing variables is gradually transferred to slower, more stable ones, preserving memories against overwriting.
The model’s key innovation is the combination of multiple dynamical processes operating across timescales and communicating with each other. Fast processes quickly store new information, while slower processes consolidate it long term. Crucially, interactions between fast and slow variables are bidirectional, which enhances robustness. The authors show that this arrangement dramatically improves memory capacity: capacity scales almost linearly with the number of synapses, a substantial improvement over prior models whose capacity scaled with the square root of synapse number.
Drs. Benna and Fusi expect this theoretical framework to assist experimental neuroscientists by suggesting specific molecular or circuit-level mechanisms to test. It also explains several observed features of biological memory, including delayed synaptic changes, metaplasticity (the plasticity of synaptic plasticity), and the benefit of spaced learning.
The technological implications are promising as well. Dr. Fusi has long been interested in neuromorphic computing—electronic systems that emulate brain-like architectures. “Current neuromorphic hardware can have severely limited effective memory capacity when designed to learn autonomously,” he noted. “A better model of synaptic memory could help overcome those limits, enabling compact, energy-efficient devices with improved learning performance.”
“Although the synaptic basis of memory is well-established, clarifying how synapses maintain memories over many years without degradation has been challenging,” said Dr. Abbott. “The model developed by Drs. Benna and Fusi offers a concrete computational guide for researchers investigating the molecular complexity of synapses.”
Funding: This research was supported by the Gatsby Charitable Foundation, the Simons Foundation, the Swartz Foundation, the Kavli Foundation, the Grossman Foundation, and Columbia’s Research Initiatives for Science and Engineering (RISE).
The authors report no financial or other conflicts of interest.
Source: Anne Holden, Zuckerman Institute.
Image credit: Fusi Lab/Columbia University’s Mortimer B. Zuckerman Mind Brain Behavior Institute.
Original research: “Computational principles of synaptic memory consolidation” by Marcus K. Benna & Stefano Fusi in Nature Neuroscience. Published online October 3, 2016. DOI: 10.1038/nn.4401.
Computational principles of synaptic memory consolidation
Memories are stored and retained through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these interactions, the authors construct a broad class of synaptic models that harness biological complexity to preserve many memories and protect them from overwriting. Memory capacity in these models scales nearly linearly with the number of synapses, a substantial improvement over the square-root scaling of earlier models. This improvement arises from combining multiple dynamical processes that initially store memories in fast variables and progressively transfer them to slower variables, with bidirectional interactions between fast and slow components. The proposed models are robust to parameter changes and account for features of biological memory, including delayed expression of synaptic modifications, metaplasticity, and spacing effects.
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