Modeling Alzheimer's Disease: From Memory Loss to Plaque & Tangles Formation

TL;DR

The Hopfield model is employed as a simplified framework to explore both the memory deficits and the biochemical processes characteristic of Alzheimer's disease and suggests that both neuronal degradation and metabolic factors contribute to the progressive decline seen in Alzheimer's disease.

Abstract

We employ the Hopfield model as a simplified framework to explore both the memory deficits and the biochemical processes characteristic of Alzheimer's disease. By simulating neuronal death and synaptic degradation through increasing the number of stored patterns and introducing noise into the synaptic weights, we demonstrate hallmark symptoms of dementia, including memory loss, confusion, and delayed retrieval times. As the network's capacity is exceeded, retrieval errors increase, mirroring the cognitive confusion observed in Alzheimer's patients. Additionally, we simulate the impact of synaptic degradation by varying the sparsity of the weight matrix, showing impaired memory recall and reduced retrieval success as noise levels increase. Furthermore, we extend our model to connect memory loss with biochemical processes linked to Alzheimer's. By simulating the role of reduced insulin sensitivity over time, we show how it can trigger increased calcium influx into mitochondria, leading to misfolded proteins and the formation of amyloid plaques. These findings, modeled over time, suggest that both neuronal degradation and metabolic factors contribute to the progressive decline seen in Alzheimer's disease. Our work offers a computational framework for understanding the dual impact of synaptic and metabolic dysfunction in neurodegenerative diseases.

Figures (4)

• Figure 1: Neuronal and Synaptic Degradation in Normal vs. Alzheimer’s Brain. The left panel shows a representation of neurons in a normal brain, with intact synaptic connections. The right panel illustrates neurons in an Alzheimer’s brain, displaying hallmark pathological features, including red dots representing amyloid plaques and green dots representing neurofibrillary tangles. Synaptic loss is also highlighted, indicating the disruption in communication between neurons that is characteristic of Alzheimer’s disease.
• Figure 2: Successful Memory Retrieval as a Function of Stored Patterns with Varying Noise Levels. The curves represent the best-fit retrieval probabilities for different levels of noise added to the initial attractor state, with noise levels c = 0.5, 1, 2, and 3. As the number of stored patterns increases, successful retrieval decreases more rapidly for higher noise levels. The theoretical network capacity, 35 patterns, is marked to indicate the maximum number of patterns that can be stored with high retrieval accuracy in a noise-free condition. Increased noise leads to earlier retrieval failures, simulating cognitive confusion as Alzheimer’s progresses.
• Figure 3: Impact of Synaptic Degradation on Memory Retrieval as a Function of Stored Patterns. The degradation is simulated by multiplying the synaptic weight matrix by a sparsity matrix with probabilities f = 0.9, 0.8, 0.7, 0.6, and 0.5, where f represents the fraction of remaining synaptic connections. As the probability f decreases, indicating increased synaptic loss, the probability of successful memory retrieval declines more sharply with an increasing number of stored patterns. This result reflects how synaptic degradation in Alzheimer’s disease impairs memory function, leading to retrieval failure as neuronal connections weaken.
• Figure 4: Linking Insulin Sensitivity to Calcium Influx, Misfolded Proteins, and Plaque Formation Over Time. The top left plot depicts the gradual decrease in insulin sensitivity over a decade, while the top right plot illustrates the corresponding increase in calcium influx into mitochondria from mitochondria-associated membranes (MAMs) as a function of time. The bottom left plot shows the accumulation of misfolded proteins over time, and the bottom right plot depicts the formation of amyloid plaques as a function of time. Together, these plots demonstrate how metabolic dysfunction, specifically reduced insulin sensitivity, can drive the biochemical processes leading to protein misfolding and plaque formation, contributing to the progression of Alzheimer’s disease.