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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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Fine-Tuning Of Neuro-exocytosis by Two Members of The Pi3-Kinase Family: Type-I PI3Kdelta And Type-II PI3K-C2alpha

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Dr. Rishabh Pathak

Fine-tuning of neuroexocytosis by two members of the PI3-kinase family, Type-I PI3Kdelta and Type-II PI3K-C2alpha, involves intricate signaling pathways that regulate various aspects of synaptic vesicle release and neurotransmitter secretion. Here is an overview of how these PI3-kinase isoforms contribute to the fine-tuning of neuroexocytosis:


1.      Type-I PI3Kdelta:

o    Regulation of Neurotransmitter Release: Type-I PI3Kdelta is involved in modulating neurotransmitter release at the presynaptic terminal.

oPhosphoinositide Signaling: PI3Kdelta phosphorylates phosphatidylinositol 4,5-bisphosphate (PIP2) to generate phosphatidylinositol 3,4,5-trisphosphate (PIP3), a key signaling molecule.

o    Vesicle Priming: PI3Kdelta activity influences vesicle priming and docking, preparing synaptic vesicles for fusion and exocytosis.

o Calcium Dynamics: PI3Kdelta-mediated signaling pathways interact with calcium-dependent processes that regulate synaptic vesicle release.

2.     Type-II PI3K-C2alpha:

o    Role in Neuroexocytosis: Type-II PI3K-C2alpha plays a specific role in regulating neuroexocytosis and synaptic transmission.

o    Phosphoinositide Metabolism: PI3K-C2alpha is involved in the metabolism of phosphoinositides, including PIP2 and PIP3, at the presynaptic membrane.

o    Synaptic Vesicle Dynamics: PI3K-C2alpha activity influences synaptic vesicle trafficking, endocytosis, and recycling processes.

o    Regulation of Fusion Machinery: PI3K-C2alpha may interact with proteins involved in the fusion machinery of synaptic vesicles, fine-tuning the release of neurotransmitters.

3.     Interplay Between PI3K Isoforms:

o    Complementary Functions: Type-I PI3Kdelta and Type-II PI3K-C2alpha may act synergistically or in parallel to regulate different aspects of neuroexocytosis.

o    Cross-Talk with Signaling Pathways: These PI3K isoforms may cross-talk with other signaling pathways involved in synaptic transmission, such as calcium signaling and protein kinase cascades.

o    Dynamic Regulation: The activity of PI3K isoforms is dynamically regulated in response to neuronal activity and synaptic inputs, allowing for precise control of neurotransmitter release.

4.    Implications for Synaptic Plasticity:

o    Synaptic Strength: Fine-tuning neuroexocytosis by PI3K isoforms contributes to the regulation of synaptic strength and plasticity.

o    Long-Term Potentiation: Modulation of neurotransmitter release by PI3K signaling pathways may impact long-term potentiation (LTP) and other forms of synaptic plasticity.

o    Neuronal Communication: Proper functioning of PI3K isoforms is essential for efficient neuronal communication and synaptic efficacy in neural circuits.

Understanding the roles of Type-I PI3Kdelta and Type-II PI3K-C2alpha in fine-tuning neuroexocytosis provides insights into the molecular mechanisms underlying synaptic transmission and synaptic plasticity. Dysregulation of PI3K signaling pathways may contribute to synaptic dysfunction and neurological disorders, highlighting the importance of these kinases in maintaining proper neuronal function.

 

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