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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Functions Of APC/C-CDH1 In Postmitotic Neurons

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Dr. Rishabh Pathak

The Anaphase Promoting Complex/Cyclosome-Cdh1 (APC/C-Cdh1) is a multiprotein complex known for its role in cell cycle regulation, specifically in targeting cell cycle proteins for degradation during mitosis. However, recent studies have revealed novel functions of APC/C-Cdh1 in postmitotic neurons. Here are some key points regarding the functions of APC/C-Cdh1 in postmitotic neurons:


1.      Neuronal Survival:

o Cyclin B1 Degradation: In postmitotic neurons, APC/C-Cdh1 promotes the continuous degradation of cyclin B1, a key cell cycle regulator. By targeting cyclin B1 for proteasomal degradation, APC/C-Cdh1 prevents its nuclear accumulation and inhibits cell cycle re-entry, thereby promoting neuronal survival.

o Apoptosis Regulation: Dysregulation of APC/C-Cdh1-mediated cyclin B1 degradation in postmitotic neurons can lead to aberrant cell cycle activation and apoptosis. Maintaining proper APC/C-Cdh1 activity is crucial for preventing neuronal cell death and ensuring long-term neuronal survival.

2.     Axonal Growth and Synaptogenesis:

o    Regulation of Developmental Processes: APC/C-Cdh1 has been implicated in regulating axonal growth and synaptogenesis in postmitotic neurons. By controlling the degradation of specific proteins involved in neuronal development, APC/C-Cdh1 influences the structural and functional maturation of neurons.

o Synaptic Connectivity: Proper functioning of APC/C-Cdh1 is essential for establishing and maintaining synaptic connectivity in the brain. Disruption of APC/C-Cdh1 activity can impact synaptic plasticity and neuronal network formation, potentially leading to cognitive deficits.

3.     Glucidic Metabolism:

o Metabolic Regulation: APC/C-Cdh1 has been linked to the regulation of glucidic (carbohydrate) metabolism in postmitotic neurons. By modulating the stability of metabolic enzymes or regulators, APC/C-Cdh1 may influence energy production and utilization in neurons, thereby impacting neuronal function and viability.

o    Metabolic Homeostasis: Maintaining metabolic homeostasis is crucial for neuronal health and function. APC/C-Cdh1-mediated control of glucidic metabolism pathways in postmitotic neurons highlights the diverse roles of this complex beyond cell cycle regulation.

4.    In Vivo Studies:

o Mouse Models: Studies using specific neuronal knockout mouse models for Cdh1 have demonstrated the importance of APC/C-Cdh1 in neuronal survival in vivo. Depletion of Cdh1 in the brain leads to selective neuronal loss, emphasizing the essential role of APC/C-Cdh1 in maintaining neuronal integrity and function.

o Layer-Specific Effects: Cdh1 depletion in the cerebral cortex results in a time-dependent shortening of specific cortical layers, indicating a progressive loss of neurons. These in vivo findings underscore the significance of APC/C-Cdh1 in preserving neuronal populations and cortical architecture.

In conclusion, APC/C-Cdh1 plays critical roles in postmitotic neurons beyond its canonical function in cell cycle regulation. By influencing neuronal survival, axonal growth, synaptogenesis, and metabolic processes, APC/C-Cdh1 contributes to the maintenance of neuronal integrity and function. Understanding the diverse functions of APC/C-Cdh1 in postmitotic neurons provides insights into the molecular mechanisms underlying neuronal development, connectivity, and metabolic homeostasis, with implications for neurodegenerative disorders and cognitive function.

 

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